structured investment product - construction, backtesting and analysis

Structured Investment Products

FI6022: Financial Engineering

Niall Gilbride 09008201

Garry Lynch 0871117

Evan Ryan 14106523

Barry Sheehan 0854867

MSc. in Computational Finance

2015

Title Page

University: University of Limerick

Program: MSc. in Computational Finance

Year of Submission: 2015

Authors: Garry Lynch, Niall Gilbride, Evan Ryan, Barry Sheehan

Title: Structured Investment Products

Lecturer: Dr. Bernard Murphy

This assignment is solely the work of the authors and submitted in partial fulfilment of the

requirements of the MSc. in Computational Finance.

XGarry Lynch, Niall Gilbride, Evan Ryan, Barry S...

MSc. in Computational Finance Candidates

Contents

Title Page ................................................................................................................................... 2

Project Overview: ...................................................................................................................... 4

Section 1: 5 Year Auto-callable Note: ...................................................................................... 4

1.1 Introduction: ................................................................................................................... 4

1.2 Auto-Callable Note Creation: .......................................................................................... 6

1.3 Auto-Callable Note Performance Backtest: ..................................................................... 6

1.4 Auto-callable Note Benchmark: ..................................................................................... 9

1.5 Risk-Return Trade-off Analysis:.................................................................................... 16

1.6 Auto-callable Note Conclusion: ..................................................................................... 22

Section 2: Ladder Forward Structured Investment Product: .................................................... 24

2.1 Introduction: ................................................................................................................... 24

2.2 Engineering Ladder Forward Position: .......................................................................... 25

2.3 Long Ladder Call ........................................................................................................... 26

2.4 Short Ladder Put ............................................................................................................ 28

2.5 Backtest LF Performance over 1st January 2008 – 31

st December 2011: ...................... 30

2.6 2RLC and 2RLC Payoff Validation:.............................................................................. 32

2.7 Ladder Forward Replicating Portfolio Benchmarking: ................................................. 33

2.8 Risk-return Tradeoff Analysis – Downside Capital Loss Protection: ........................... 34

2.9 Collar Backtest over 01/01/2008 – 12/31/2011: ............................................................ 35

Appendix 1: Payoff Calculations for Autocallable Note Structured Investment Product .... 38

Appendix 2: Payoff Calculations for Long Ladder Forward ................................................... 39

Appendix 3: Payoff Calculations for Long Ladder Forward with Cap and Floor ................... 40

Appendix 4: Marketing Brochure for Auto-callable and Long Ladder Forward Structured

Investment Products ................................................................................................................. 41

Appendix 5: Matlab Code ........................................................................................................ 42

Project Overview:

The aim of this project is to develop a comprehensive and intuitive understanding of the

financial engineering behind structured investment products, namely Auto-callable Notes and

the Ladder Structured Forward. According to (McCann, 2006), such structured products gained

enormous popularity amongst market participants with almost $50 billion of such structured

products being sold in 2005 alone. The National Association of Securities Dealers (NASD) re-

enforced this with their member address in April 2005 claiming “In the current investment

environment, investors and brokers are increasingly turning to alternatives to conventional

equity and fixed income investments in search of higher returns or yields”. The rationale

behind such an increase came in the form of an enhanced yield quest from investors alongside

misleading marketing campaigns from some the most evocative names in finance such as

Citigroup.

Through the use of emphasis and exaggeration such firms could highlight positive elements to

such product compositions for example “protection feature”, “enhanced coupon”, and worst

case flat market scenarios as per (Citigroup, 2007), such respected institutions were able to

attract investors without highlighting the inherent risks associated with such products which

according to (McCann, 2006) “are often complex or have unique features that may not be fully

understood by the retail customers to whom they are frequently offered, or even by the brokers

who recommend them”, a point complementing the litigation issues being faced by the likes of

Davy pointed out by (Murphy, 2015).

Such market participants have exposed by the Financial Industry Regulatory Authority

(FINRA) for appearing “to offer benefits to investors that are already available in the market

in the form of less risky or less complicated products” bringing concerns to light about the

suitability and potential conflicts of interest regarding such products. We financially engineer a

5 year Auto-callable Note and a 5 year Ladder Structured Forward for the reference period 1st

January 2008 to 31st December 2012 for the Standard and Poor’s 500 Index, benchmarking and

back-testing throughout providing high net worth individual investors (HNWI) with a

transparent and comprehensive analysis into the risk-return trade-off associated with such

products and a client-specific suitability determination for each product.

Section 1: 5 Year Auto-callable Note:

1.1 Introduction:

The auto-callable note is very similar to the reverse convertible note in that it pays an enhanced

coupon to the investor as compensation for exposing the investor’s capital to higher levels of

risk than that of a plain vanilla instrument. The enhanced coupon element stems from the

amortization of a sold at-the-money (ATM) put option. Unlike the reverse note, the auto-

callable can be retired early on any of the associated annual anniversary dates, this retirement

happens in an autonomous manner. The objective of this product is to generate such an

enhanced coupon for the investor whilst providing a contingent protection in an attempt to

preserve capital employed.

The auto-callable note endeavours to provide this superior coupon by setting two barriers (1)

an auto-call barrier and (2) a lower protection barrier. The interaction between the underlying

index price and the barrier levels will dictate the investors’ payoff. For the purposes of this

project we will use the discrete style auto-callable note whereby payoffs will be determined by

the underlying index level at the annual anniversary redemption dates. If the underlying index

exceeds the auto-call barrier at an anniversary date, the investor will get the face-value and

enhanced coupon for the specified time period and the product will cease to exist. If the

underlying index fails to hit the barrier at an anniversary redemption date no coupons will be

paid and provided that the protection barrier has not been breached, face-value will be

redeemed at maturity without coupons (See Figure 1). Should the lower protection barrier be

breached during the lifespan of the product, significant losses are a possibility for the investor

depending on the index level at future redemption dates.

Auto-callable products tend to be issued for longer time horizons than their reverse-convertible

counterparts. For this reason in addition to the lack of clarity with regard to coupon

entitlements and potential losses arising from a protection barrier breach we recommend such a

product for a high net worth individual investor with a risk-taking appetite, low investment

liquidity concerns (given that face-value redemption may not occur until maturity) and a full

awareness of the potential losses that could be incurred given a lower barrier breach.

Figure 1: Auto-callable Payoff Structure

1.2 Auto-Callable Note Creation:

For the purposes of this project, a 5 year auto-callable note is created for the S&P500 (SPX)

index for the reference period 1st January 2008 to 31

st December 2012 using the Option

Valuation Structured Note Auto-Callable (OVSN AC) function in Bloomberg Terminal. The

Auto-Call barrier was set at 105%, with a contingent coupon of 10%, a Lower protection

barrier of 55% (continuously active), with an early redemption and participation value of 100%

as evident in Figure 2. The annual anniversary dates can be seen in figure 2 as being the 31st of

December 2008, 2009, 2010 and 2012 and the 30th

of December 2011 with the valuation date

being 1st of January 2008 as per our brief.

1.3 Auto-Callable Note Performance Backtest:

Figure 3 highlights how the auto-callable note created performed during its lifespan. It is

evident that the 105% Auto-call barrier was never breached meaning that the investor received

no coupons throughout the lifespan of the product, this also means that the + 5Y 0%/105%

Knock-Out put did not provide a face value to the investor and emphasizes the need to

purchase the + 5Y 0%/0% Knock-Out put in order to ensure a face value at maturity.

The written 100%/55% Knock-In Put was activated in 2008 exposing the investor to some

major downside risks should the put expire in the money at maturity. In this instance the

investor was fortunate in that the sold Knock-in put expires out of the money as the index

begins to rally from 2009 onwards meaning that at expiry the liability to the investor with

regard to the amortized put was $0.

At expiry the SPX level was $1426.19 compared to a starting value of $1447.16 on the 1st of

January 2008, for this reason, the investor made a capital loss due to the fact that the +5Y

0%/105% Knock-out Put was unable to provide a 100% face value as the 105% barrier was

never breached. Instead, the guaranteed face value at maturity +5Y 0%/0% Knock-out put for

year 5 delivered a face value of $1426.19 which in addition to zero coupons left the investor

with a payoff of the difference between ST and S0 which is $1426.19-$1447.16 = -$20.97

notionally, or 100-98.69 = -1.31 according to the normalized returns (See Section 1.4).

Figure 2: OVSN Auto-Callable Creation

As mentioned in Section 1.1, the payoff of this discrete style auto-callable note will be

determined at annual anniversary dates. If the index level lies above the auto-call level (105%

in this instance) on an annual anniversary date (See Table 1), the note will be auto-called at

that date for 100% face value along with any deferred contingent coupons ( ). In the case

of our SPX Auto-callable the 105% auto-call barrier is not breached meaning we do not

receive any coupons and in fact make a capital loss of 1.31% as mentioned above. Figure 4

demonstrates how the annual redemption date values must breach the green 105% auto-call

level on these specific dates in order for the note to retire early with enhanced coupons and

100% face value.

Table 1: Auto-callable Note Annual Anniversary Summary

Year Date Price Normalized

Y1 12/31/2008 903.25 59.12

Y2 12/31/2009 1115.1 76.62

Y3 12/31/2010 1257.64 89.57

Y4 12/30/2011 1257.6 89.51

Y5 12/31/2012 1426.19 98.69

01/01/08-12/31/12 Annual Anniversary Date Summary

Figure 3: Back-Testing of Performance of the Auto-callable Note for the Reference Period

Figure 4: Annual Anniversary Redemption Dates

Component Type

1 Discrete

2 Discrete

2 Discrete

3 Continous To earn an enhanced coupon

Replicating Portfolio for the Auto-Callable Note SPX (105%/55%)

Instrument

Long 5 Year (0% Strike/105% Barrier) Knock-out Put

Long 5 Year (0% Strike/105% Barrier) Knock-out Put (Active for Y1-4)

Long 5 year (0% Strike/0% Barrier) Knock Out Put (Active for Y5 only)

Short 5 Year (100% Strike/55% Barrier) Knock In Put

Purpose

To earn n*C contingent coupons

To provide a FV of 100%

To ensure a FV at maturity

1.4 Auto-callable Note Benchmark:

Replicating Portfolio Construction:

The Auto-callable Note structured investment product has three key constituents in its

composition (See Table 2). Component 1 consists of a long knock-out put with a strike of 0%

and a barrier of 105% which earns discrete contingent based cash rebates (n*Ce) on

designated annual anniversary redemption dates which in this instance is the 31st of

December with the exception of 2011 where the anniversary redemption date is 30th

of

December.

Component 2 of the structured product is made up of a long 5 year 0% strike 105% barrier

knock-out put and a long 5 year 0% strike 0% barrier knock-out put. The long 0%/105%

knock-out put in component 2 barriers span the first four years of our product and combines

with component 1 in order to cater for early retirement of the note. For instance, should the

index level lie above the auto-call barrier of 105% on the 31st of December years 1-4, the full

face value and n*Ce (n = years, C

e= enhanced coupon) deferred contingent coupons will be

redeemed to the investor and the note will cease to exist (automatically called to retirement).

Should the index not breach the 105% barrier on an anniversary date years 1-4, the investors’

face value is put at risk. The long 5 year 0%/0% knock-out put ensures a face value is

returned to the investor come maturity of the note in an economical manner as the 0%/0% put

is the cheapest knock-out put we can purchase to provide the rebate (See Figure 5).

Component 3 consists of a short 5 year 100% strike 55% barrier knock-in put with no cash

rebates. This component is the source of our enhanced coupon and the primary source of risk

to the investors’ capital. Should this put be knocked-in and expire in the money, the investor

will receive a face value of (

) . For example, if the index finishes at year 5 at 70%

of its initial value with the lower barrier knocked in, the shorted knock-in put will finish 30%

in the money at expiry, the investor will receive 70% of their face value hence the major risks

associated with such products originates from the sold 100%/55% put in an attempt to

increase coupon payments. This payoff can also be denoted as:

Following the above example, with the knock-in put finishing 30% in the money the face

value payoff is as follows:

Table 2: Replicating Portfolio of Auto-Callable Note

Using the OVSN function of Bloomberg Terminal, the SPX Auto-callable was calculated

with a valuation date of 31st of December 2012 using the identical contingent coupon levels,

auto-call barrier, lower soft protection barrier, and strike price as Section 1.2 for a notional

amount of $100, a strike date of 01/02/2008 and a maturity date of 12/31/2012 as per

(Murphy, 2015) and can be seen in Figure 6 below. Daily last price data for the reference

period was then downloaded from Bloomberg Terminal, normalized in Matlab and used to

perform a replicating portfolio back-test and performance analysis. Figures 7 and 8 show a

validated replicating portfolio as evident by an identical payoff consisting of zero coupons,

and a normalized maturity face value of 98.69 consistent with Bloomberg. The normalized

payoff formula additionally validates the figure with a capital loss of 1.31%:

[

]

Figure 5: 0%/0% Knockout-Put Cheapest Means of Ensuring a Face Value

Figure 6: OVSN AC Price Calculation 12/30/2012

Actual SPX 100 100 100 100 100 100

55% 105% Price Series 2008-2012

Protection Autocall (Normalised)

Barrier Barrier Drift s e (t) S(t) t

55 105 0.0% 15% 100.0 0

55 105 0.65 100.0 1

55 105 0.33- 97.5 2

55 105 2.45- 97.9 3

55 105 1.67 96.1 4

55 105 0.07 97.4 5

55 105 0.40 98.1 6

55 105 0.37 96.8 7

55 105 2.37 97.9 8

55 105 2.79 95.4 9

55 105 0.77- 94.9 10

55 105 2.78- 92.1 11

55 105 2.31 91.6 12

55 105 0.82- 90.6 13 There were 1258 trading or business days in the 5Y period 01/01/2008-12/31/2012.

55 105 2.77 92.5 14

55 105 1.42 93.4 15 Trade Day 252 504 756 1008 1258

55 105 1.26 91.9 16 Excel Row No. 257 509 761 1013 1263

55 105 2.97 93.6 17 n Y1 Y2 Y3 Y4 Y5 Min{St} Max{St}

55 105 2.33- 94.1 18 S(t) 62.4 77.1 86.9 86.9 98.69 46.75 101.3

55 105 2.92 93.7 19 C(t) 10% 20% 30% 40% 50%

55 105 2.50 95.3 20 Coupons - - - - - ……………………………….

55 105 0.28- 96.4 21 Early Redemption - - - - ……………………………….

55 105 2.72 95.4 22 Final Redemption 100 ……………………………….

55 105 0.50 92.4 23 1.31- ……………………………….

55 105 1.33 91.7 24 Total Payment - - - - 98.69

55 105 0.38- 92.4 25 100.0- - - - - 98.69

55 105 2.85 92.0 26 Autocall Barrier 105%

55 105 2.64 92.5 27 Lower Protection Barrier 55%

55 105 0.49 93.2 28 Knock-In Put Conventional Strike 100%

55 105 2.27 94.5 29 Y5 Knock-Out Barrier 0%

55 105 2.57- 93.2 30

55 105 1.53- 93.3 31 Average Trading Day per year 252

55 105 2.51- 93.2 32

55 105 0.25- 94.0 33

55 105 0.20- 92.8 34

55 105 0.20- 93.5 35

55 105 2.36- 94.8 36

55 105 0.67- 95.4 37

35

45

55

65

75

85

95

105

115

Figure 7: Replicating Portfolio Consistent with Bloomberg Terminal

100 100 100 100 100 100

Year 1 2 3 4 5

Row No. 257 509 761 1013 1263

n Y1 Y2 Y3 Y4 Y5 Min{St} Max{St}

S(t) 62.42 77.05 86.90 86.90 98.69 46.75 101.3

C(t) 10% 20% 30% 40% 50% These are the 1. 2. and 3. Listed Components to the AC Replicating Portfolio

Coupons - - - - - ………………………………. 1. + 5Y 0%/105% Put with nxC% cash rebate (Discrete 100% Barriers Y1…Y5)

Early Redemption - - - - ………………………………. 2. + 5Y 0%/105% Put with FV=100% cash rebate (Discrete 100% Barriers Y1…Y4)

Final Redemption 100 ………………………………. 2. + 5Y 0%/0% Put with FV=100% cash rebate (Discrete 0% Barrier Y5 only !)

1.3- ………………………………. 3. - 5Y 100%/50% Knock-In Put with NO cash rebate (Continuously Active 50% Barrier)

Total Payment - - - - 98.69

100.0- - - - - 98.69

Autocall Barrier 105% CAR (Compound Annualised Return) since beginning of investment

Lower Protection Barrier 55% IRR -0.3%

Knock-In Put Conventional Strike 100% Manual PV Check Calculation : 0.0 Input "Total Payment" value and Year No. as exponent

Y5 Knock-Out Barrier 0%

0

50

100

150

200

250

300

350

400

1 253 505 757 1,009 1,261

Figure 8: Replicating Portfolio Constituents alongside Auto-Callable Note Payoff

In order to convey the potential upside of auto-callable notes to investors, an auto-callable

was priced with an Auto-call barrier of 90% and a lower soft protection barrier of 40% for the

same reference period with an identical underlying index, contingent coupon rate and

notional amount. In this instance, as evident in Figure 9, the underlying index breach the

Auto-call barrier on the anniversary date of year 5 meaning the investor accumulated the

deferred contingent coupons: which amounts to plus 100% face value

due to component 2 providing a 100% cash rebate as the auto-call barrier was breached, again

the replicating portfolio is consistent with Bloomberg Terminal (See Figure 10).

Figure 9: 90% Auto-call Barrier / 40% Lower Protection Auto-callable Replicating Portfolio

Finally, to highlight the early redemption feature of such a product, the auto-call barrier is

lowered to 80% with the lower protection barrier remaining at the assigned 55% with all

other parameters remaining constant. In this instance, the note does in fact get auto-called in

year 3 and the investor can avail of prompt access to capital plus deferred coupons earning an

enhanced return ( . The note ceases to exist after year 3 and the

investor can re-invest the proceeds directly in the index as the note being called early is seen

as a bullish signal as per (Murphy, 2015) in addition to benefiting from the self-financing

aspect of the note stemming from the sold put option. Figure 11 shows the replicating

portfolio in this instance and Figure 12 shows Bloomberg Terminal Price at redemption date

for Year 3 which is consistent with the replicating portfolio.

Figure 10: 90% Auto-call Barrier/ 40% Lower Protection Bloomberg Terminal

Figure 11: Auto-call Barrier 80% / Lower Protection 55% Replicating Portfolio Payoff

1.5 Risk-Return Trade-off Analysis:

Given the fact that the lower soft protection barrier was breached in our assigned auto-

callable note structured investment product in addition to accruing a capital loss over the 5

year period it is vital that an appropriate risk-return trade-off analysis is conducted in order to

(a) gauge the viability of the product itself for investors across the board and (b) to find a

criteria for suitable investors as per (National Association of Securities Dealers, 2005). In

order to do this, we create three plausible scenarios with regard to the underlying index

market environment in which the structured product operates in. In this project, we use a

bearish, flat and bullish market scenario in contrast to the negligible flat, moderate growth

and bullish market environments as per (Citigroup, 2007) where risks were not taken into

account in the form of the sold knock-in put which as we have seen is far from immune to

activation even with low barriers such as 55% of the underlying index.

Bearish Scenario:

Using data from Bloomberg for the period 1st of January 2008 to 31

st of December 2008 it is

evident that the period was one of a bearish nature (See Figure 13). Using the daily data

extracted from Bloomberg Terminal, a daily return standard deviation was calculated to be

3% and a by scaling the annual volatility was found to be 41.0778%:

√ = 41.0778%

Figure 12: Early Redemption Year 3 with Auto-call Barrier 80% and Protection Barrier 55%

Using this annual volatility level in addition to the prescribed -10% annual drift parameter,

the likelihoods of the seven possible outcomes (See Table 3) with regard to the structured

product are evident in Figure 14. In this very realistic scenario, the true risk of these

structured products becomes apparent. Over 55% of the time, an auto-callable note with a

55% lower protection barrier and a 105% auto-call barrier will result in not being auto-called

and will incur a capital loss during bearish markets such as 2008. This is reflected in the auto-

callable structure examined in Section 1.4, the majority of this risk and potential losses stem

from the sold knock-in put being activated.

There is a mere 0.4% chance of the note returning a full face value at maturity should the

note be auto called. The chances of the note being auto-called in year 5 with 50% coupon and

capital protection is 1.2%, year 4 probability of being auto-called with 40% coupon and

capital protection is 2.4%, year 3 probability of early retirement and a 30% coupon is 3.2%,

year 2 early redemption with capital protection and a 20% coupon has a 8.4% of occurring

and the auto-call in year 1 with a 10% coupon and capital protection has a 29% probability of

coming to fruition. Clearly there are huge risks associated with such a product in a bearish

market and thus requires a clear understanding on the part of the investor towards such risks

of capital losses.

Figure 13: 1st of January 2008 to 31st of December 2008 Bearish Market

%

29

8.4

3.2

2.4

1.2

0.4

55.4

100Total Probability

Outcome

Auto-called Y1 with 10% coupon





Not auto-called with capital protection at maturity

Not auto-called with capital loss at maturity

Bearish Market Likelihood of Payoff

Figure 14: Likelihood of Various Payoff Outcomes (Bearish Scenario)

Table 3: Bearish Market Payoff Probabilities

Bullish Scenario:

Using data from Bloomberg for the period 30th

December 1994 to 30th

of December 1995 it is

evident that the period was one of a bullish nature (See Figure 15). Using the daily data

extracted from Bloomberg Terminal, a daily return standard deviation was calculated to be

0.49% and a by scaling the annual volatility was found to be 8%:

√ = 8%

Using this annual volatility level in addition to the prescribed 10% annual drift parameter, the

likelihoods of the seven possible outcomes (See Table 4) with regard to the structured product

are evident in Figure 16. In this plausible scenario, we see the payoff likelihoods radically

change with the once dominant capital loss 55.4% probability in the bearish market no longer

in existence. In this case, the most likely scenario is the 72.1% 1 year early retirement with a

10% coupon and capital protection followed by the 2 year auto-call with a 20% coupon and

capital protection. There is a 6.6% change of the investor accumulating a 30% coupon and

early redemption in year 3 and a 1.9% chance of a 40% deferred coupon and capital

protection in year 4. In fact, there is a 99.5% chance in such a market environment that the

investors’ capital and coupons will be redeemed early and a mere 0.2% chance the note will

note be auto-called however capital will remain protected. This is clearly a stark difference to

the bearish market scenario, one in which risks could easily be forgotten about leading to

investors not meeting important criteria entering into such structured products for example,

those with liquidity constraints, lack of knowledge of inherent risks and the need to preserve

capital.

Figure 15: 30th December 1994 to 30th of December 1995 (Bullish Market)

%

72.1

18.9

6.6

1.9

0.3

0.2

0

100




Total Probability

Bullish Market Likelihood of Payoff

Outcome





Figure 16: Likelihood of Various Payoff Outcomes

Table 4: Bullish Market Payoff Probabilities

Flat Market Scenario:

Due to a lack of annual flat market periods in Bloomberg, in order to find a truly flat market

annual volatility, the average of our bearish and bullish scenarios resulting in an annual sigma

of 24.5389%. Using this annual volatility level in addition to the prescribed 0% annual drift

parameter, the likelihoods of the seven possible outcomes (See Table 5) with regard to the

structured product are evident in Figure 17. Similarly, this change in market condition leads

to a drastic change in payoff probability levels. One would imagine that in a flat market

scenario, the chances of having the note not being auto-called whilst incurring a capital loss

would be somewhat negligible however Figure 17 and Table 5 highlight that it is far from

negligible with a probability of 28.8% even in a relatively calm environment given the VIX

long-run mean of 20 as per (Dash & Moran, 2005).

There is a 60.3% chance of having the note retire early in such a scenario, whereby the payoff

will be dependant of the year in which it is retired ( + Face Value. The 1 year auto-

call with a 10% coupon probability is 34.5%, the 2 year auto-call with a 20% coupon chance

of payoff is 12.6%, a year 3 early retirement with a 30% coupon is 5.9%, a 4 year auto-call

with a 40% coupon has a 3.6$ chance of occurring and the optimal year 5 auto-call with a

50% deferred coupon has an occurrence chance of 3.7% in this instance. It should be stressed

to the potential investor however that despite a 60.3% of early retirement, there is still clearly

a very high level of risk associated with the product given a 39.7% chance of not being auto-

called and a 28.8% of a capital loss again in a flat market where one would expect to remain

relatively low in terms of accruing losses given the flat nature of the environment in which

the product is operating in.

Figure 17: Likelihood of Various Payoff Outcomes (Flat Scenario)

Table 5: Flat Market Payoff Probabilities

1.6 Auto-callable Note Conclusion:

Whilst the auto-callable note structured investment product provides a number of appealing

features such as early retirement, enhanced coupons, a soft lower protection barrier and an

ability to somewhat protect capital, it became apparent from the back-testing and risk analysis

just how soft or contingent many of these features really are. The not auto-called with capital

loss at maturity payoff possibility played a large role in the bearish and flat market scenarios

(55.4% and 28.8% respectively) analysed in addition to the prescribed January 1st 2008 to

December 31st 2012 105% auto-call level/55% lower protection level auto-callable note for

the SPX. Clearly there are huge risks associated with such a product, risks that were largely

neglected in industry evident by (Citigroup, 2007) and our bullish scenario whereby the

capital loss possibility does not exist.

Investors meeting suitability criteria for such a product should be high net worth individual

investors who are actively seeking to take risk in order to earn a potentially enhanced coupon

without any liquidity concerns and who are prepared to wait for long term durations to have

their capital returned to them in addition to being prepared and fully aware of the tremendous

risks associated with the product in particularly the sold knock-in put component which can

result in capital losses over the potentially long lifespan of the structured investment. As

(National Association of Securities Dealers, 2005) point out there are alternative “less risky

or less complicated products” available on the market. If these products cannot meet the

requirements of the investor perhaps such a product could be considered solely on the basis

that the dealer is aware of the inherent risks of such a product and that this is clearly

conveyed to the potential investor who is willing to take on such additional risk in order to

compensated by a potentially enhanced reward. Figure 18 shows that 3 scenario probability

charts below, clearly the change in market environment plays a critical role in the dependant

payoffs and products which long tenures such as the auto-callable notes can and are subject to

huge risks as a consequence.

%

34.5

12.6

5.9

3.6

3.7

10.9

28.8

100




Total Probability

Flat Market Likelihood of Payoff

Outcome





Bear Market Flat Market Bull Market0

100

200

300

400

500

600

700

800

900

1000Distribution of Payoff Probabilities for 5Y Autocallable Note

Market Scenarios

Pro

bab

ilit

y %

Auto-called Year 1 with 10% coupon







Figure 18: Likelihood of Various Payoff Outcomes (Bearish/Flat/Bullish Scenarios)

Section 2: Ladder Forward Structured Investment Product:

2.1 Introduction:

A ladder option is a synthetic financial product comprised of a combination of vanilla call,

vanilla puts and barrier options. The option has a set number of moneyness levels or ‘rungs’

which if hit by the underlying instrument become deactivated and automatically lock in a

profit/loss. Hence ladder options are a form of path dependent option. A ladder option can be

understood as being similar to a lookback option. In a lookback option the payoff depends on

the maximum or minimum asset price reached during the life of the option, regardless of the

final asset price. A ladder also depends on the level of the asset price but instead of locking in

the maximum asset price achieved over the time period, this type of product locks in profits

at certain levels of moneyness.

Ladder call options are attractive to investors due to their ability to lock in upside exposure.

However these types of options are expensive and the inclusion of additional rung levels

further increases cost. To offset the price of the long ladder call we will short a ladder put,

taking a position similar to that of a classic long forward. The ladder forward will have a

similar payoff diagram to the classic long forward position with the addition of locking in

profits at a number of rung levels on the upside. Though this position also bears (pun

intended) the risk of potentially locking in downside exposure at the out-of-the-money

(OTM) rung levels of the shorted ladder put.

Figure 19: S&P500 Prices over 01/06/14 - 31/10/14

Illustrated in Figure 19 is the S&P 500 index over June to October 2014. A ladder call option

on the index would lock in a profit at the 2000 rung level. In fact if we had a ‘continuum’ of

rung levels (i.e. we could lock in profit at every increase in the level of moneyness) the ladder

option would be the equivalent of a lookback.

{ }

In the ladder call payoff formula above ‘R’ denotes the rung level of the option and ‘K’ the

strike level. Note from the payoff that if the rung level is not hit the option has the same

payoff as a regular call.

2.2 Engineering Ladder Forward Position:

Since a ladder option is a synthetic financial product composed of a combination of vanilla

call, vanilla puts and barrier options we can view these more basic financial products as the

‘building blocks’ of both the ladder call and ladder put options which will form the structured

forward product. The conventional strikes as well as the rung levels are priced based on put-

call parity. Consider two portfolios comprising of one European call option plus an amount of

cash equal to Ke-rT

and one European Put option plus one share. Both a worth max(ST,K) at

expiration but because the options are European, they cannot be exercised prior to the

exercise date. Hence the portfolios must have identical values today such that:

The forward price of the share is equal to S0e-rT

, thus if K is set equal to the forward price

these value will cancel out and leave us with the call equalling the put. Since we are long the

call and short the put setting up our position in this way will allow the prices of the offsetting

positions to cancel out reducing the market value of our portfolio to zero, creating what is

known as a ‘zero-premium’ option strategy. The same principle holds up for the barrier levels

which will be set equidistant from each other each side of the forward price (which is equal

the strike).These types of investment product are primarily aimed at the risk neutral type of

investor. A risk neutral investor will invest in an asset whose expected yield per unit is

greater than or equal to its price per unit (Dow, et al., 1992). Thus the marketing of this type

of financial product will be based upon the ‘zero premium’ nature of our investment product

and the positive market environment present at the beginning of 2008.

Due to the negative relationship between stock price returns and volatility (Glosten, et al.,

1993) and our products built in feature of locking in downside losses at the lower rung levels,

the 5Y Ladder Structured Forward is best suited to a low volatility market environment;

hence it’s appropriateness to more risk-averse type investors. This type of structure

investment product is perfectly tailored to the stable bull market observed by the S&P 500

prior to its launch at the beginning of 2008. Even a slowdown in the economy followed by a

slight downturn in the coming years would not adversely affect the performance of the

product if it hits one of its designated upside rung levels in the interim.

In order to cater to more risk-averse individuals we can also very cheaply minimise the

overall losses of the structured investment product by also maximising its profits by way of a

‘cap’ and ‘floor’. These will be incorporated into the position by purchasing a deep OTM put

(floor) and selling a deep OTM long call (cap). It should be noted though that the OTM put

will likely be priced at a premium to the equivalent OTM call due to the negative skew of the

S&P 500 (Heston, 1993). However this additional cost may be offset by selling the cap

slightly closer to the money than the floor.

2.3 Long Ladder Call:

Figure 20: Long Ladder Call Payoff

Label Component Description

1 +C(X=S) Basic underlying put structure

2 -P(X=S)+P(X=R1) Vanilla put spread spanning [S,R1] strike interval

3 -P(X= R1)+P(X=R2) Vanilla put spread spanning [R1,R2] strike interval

4 +PKO

(X=S,XOS

=R1)

- PKO

(X=R1,XOS

=R1)

Knockout put spread spanning [S,R1] strike interval

5 +PKO

(X=R1,XOS

=R2)

- PKO

(X=R2,XOS

=R2)

Knockout put spread spanning [R1,R2] strike interval

Table 6: Long Ladder Call Constituent Components

As illustrated in Figure 20 the long ladder call works by locking in profits as the barrier

levels at R1 and R2 are hit by the path dependant price of the underlying. Take for example

the barrier level at R1 created by the vanilla put spread and the knockout put spread both

spanning the [S,R1] strike interval. Before the asset price reaches R1 these components payoff

structures cancel each other out. If R1 is hit the knockout put spread, labelled ‘4’ in Figure

20, is knocked out. If the value falls back below R1 the knockout put spread is no longer

active to cancel out the positive payoff of the vanilla put spread (labelled ‘2’ in Figure 20)

and thus this spread locks in a profit equal to max(R1 –ST,0), however the profit is capped at

10. A profit of 10 will always be locked in even if the asset price falls does not subsequently

fall below the strike as the remainder will be made up by the long call represented as ‘1’ in

Figure 20.

The same logic applies to the R2 rung level and the payoff for the entire long ladder call may

be represented as:

{ }

Where represents the highest rung level achieved. If both rung levels are hit and the asset

price is below R2 the payoff will be R2-K. If the asset price finished above R2 then from

Figure 20 we can see that positions 2-5 will all be worthless and the payoff will simply be

ST-K. Conversely if no barriers are hit then positions 2-5 will all cancel each other out and

the payoff will be max(ST-K,0).

Figure 21: Two Rung Ladder Call

Figure 21 illustrates the two rung ladder call (2RLC) created in Bloomberg. The market

value of the position is illustrated by the yellow line while the intrinsic value is the green line.

The product is priced at-the-money forward to take advantage of put-call parity and create a

‘zero-premium’ structured product when the 2RLC is combined with a short position in a two

rung ladder put Note the high cost of this position on the y-axis. If the 2RLC were used as a

stand-alone investment product the investment would start life at a loss due to the high

premium of the position. Hence the offsetting short of a two rung ladder put which recoups

the cost of the 2RLC, but also introduces downside risk.

There is a distinctive upturn in the market value of the 2RLC as it approaches each rung

level. These ‘kinks’ are highlighted in Figure 21 above and reflect the 2RLC feature whereby

once the asset price reaches the rung level it deactivates one of the offsetting knockout

spreads and thus locks in a profit in the call spread spanning that strike interval. Hence as the

asset price gets closer to R1 and R2 the higher likelihood of locking in a profit is reflected by

the upturn (kink) in the market value of the position. A feature of these kinks is that closer to

the money rung levels become more pronounced than the other rung level kinks the closer the

option gets to expiry. This is obviously reflecting the higher chance of only hitting a closer to

the money rung level at the expiry date approaches.

The slight drop off in market value which is noticeable in Figure 21 after each rung level is

hit doesn’t mean that the position is falling in value. Rather this decrease in slope reflects the

fact that the 2RLC is priced at an ever reducing premium to a regular vanilla call (which is

not shown in Figure 3 but would asymptotically track the intrinsic value line below the

market value of the 2RLC).

2.4 Short Ladder Put:

Figure 22: Short Ladder Put Payoff

Since we are short the ladder put the payoff diagram in Figure 22 is inverted. This is obvious

almost immediately from the fact that the long put in described in Table 7 is illustrated as a

short put position in Figure 22.

Label Component Description

1 +P(X=S) Basic underlying put structure

2 -C(X=S)+C(X=R1) Vanilla call spread spanning [S,R1] strike interval

3 -C(X= R1)+C(X=R2) Vanilla call spread spanning [R1,R2] strike interval

4 +CKO

(X=S,XOS

=R1)

- CKO

(X=R1,XOS

=R1)

Knockout call spread spanning [S,R1] strike interval

5 +CKO

(X=R1,XOS

=R2)

- CKO

(X=R2,XOS

=R2)

Knockout call spread spanning [R1,R2] strike interval

Table 7: Long Ladder Put Constituent Components

In this scenario it is our positions losses are covered by the knockout call spreads (4 and 5)

which offset the losses accrued from the vanilla call spreads (1 and 2). If the barrier levels at

R1 and R2 are breached the offsetting knockouts will be deactivated and thus will no longer

offset the losses associated with the vanilla put spreads. Hence if the downside rung levels are

breached our position will lock in downside losses in the same way it locks in upside profit.

The payoff function for the short ladder put is given by:

{ }

Note that both Table 6 and Table 7 two contain nine ‘building blocks’ through which we

created the long ladder call and short ladder put components of our structured investment

product. However the long and short vanilla puts at the first rung level of the long ladder call

effectively cancel each other out and this component of the product can be built with a single

call spread spanning the interval [S,R2]. The same applies to the long and short vanilla calls at

the first rung level in the short ladder and this is in fact how each component of the structure

investment product was constructed, i.e. with 7 ‘building blocks’ instead of 9.

Figure 23: Two Rung Ladder Put

Figure 23 illustrates the two rung ladder put (2RLP) component of our long ladder forward

position. In our structured investment product we will be shorting the 2RLP and the payoff

illustrated in Figure 23 will be inverted. Like the 2RLC note the high premium on the y-axis

associated with this component, however the corresponding 2RLP is itself priced at a

premium to the 2RLC as is evident on the y-axis of both graphs. This discrepancy arises from

the negative skew of the S&P 500 index returns resulting in far OTM put options being

priced at a premium to far OTM calls (Heston, 1993). This in fact creates the opportunity for

the engineers of these type of forward investment products to set the downside rung levels

further from the money than the upside rung levels and still create a ‘zero-premium’

investment product with lower risk of locking in downside profits.

Alternatively the upside rung levels could be set closer to the money improving the

investments chances of locking in a profit while maintaining the same level of downside risk.

Alternatively the profit accrued straight away from shorting the 2RLP could be retained by

the company providing these types of investment product and used to fund the enhanced yield

of an auto-callable note, enabling the short put in that financial product to be set a lower level

reducing the risk associated with that type of investment product.

There is also a cumulative effect associated with the ladder options automatic profit lock in

feature. As a result as more rungs are added to the product the financial engineer will observe

the market value line discernibly move ever higher above the intrinsic value up until the final

rung is reached. After this point as the asset price move even higher the ever increasing

intrinsic value of the position becomes the dominant feature in the payoff and as a result in

both Figure 21 and Figure 23 we observe the market value of the respective 2RLP and 2RLC

components asymptotically approach the intrinsic value of the long ladder forward structured

investment product.

Figure 24: Long Ladder Forward

Illustrated in Figure 24 is the combined 2RLC and 2RLP, resulting in a two rung ladder

forward. The various rung levels are indicated and materialise as distinctive ‘kinks’ in the

near dated (7 days to expiry) payoff.

2.5 Backtest LF Performance over 1st January 2008 – 31

st December 2011:

Figure 25: SPX over backtest period with 2RLP rung levels

The long ladder forward was back tested over the period: 01/02/2008-12/31/2011. Figure 25

illustrates the SPX over the back-test period. The ATMF price at the end of the back test

period was $1581.30. The two rung levels for the 2RLP are indicated on the graph, while the

scale of the graph prohibited the inclusion of the two 2RPC rungs.

The 2RLC deal was opened in OVME. The dates of expiry were changed to the end of the

back test period, i.e. 12/31/2011 and the strike level changed to the ATMF price on the end

date, i.e. $1,581.30. The rung levels were set as: R1=$1739.43 (110% ATFM) and

R2=$1897.56 (120% ATMF). This is illustrated in the OVME screenshot in Figure 26.

Figure 26: 2RLC OVME backtest

The 2RLP deal was also opened in OVME. The expiry date was changed to 12/31/2011 and

the strike level changed to the ATMF price on the end date, i.e. $1,581.30. The rung levels

were set at R1=$1423.17 (90% ATFM) and R2=$1265.04 (80% ATMF). This is illustrated in

the OVME screenshot in Figure 27.

Figure 27: 2RLP OVME backtest

The two deals were saved in OSA, as illustrated in Figure 28.

Figure 28: OSA payoff profile of 2RLC and 2RLP

2.6 2RLC and 2RLC Payoff Validation:

The payoff for the 2RLC is as follows:

[ { } ]

Where, ST=$1257.60 (the stock price at the end of the back test period), R1=$1739.43 (the

first rung level), R2=$1897.56 (the second rung level) and K=$1581.30 (ATMF on the end

date of the back test period). Substituting in the appropriate values:

{ }

No rung levels were hit, thus:

0

This is confirms the 2RLC payoff demonstrated in Figure 28.

The payoff for the 2RLP is as follows:

{ }

Where, ST=$1257.60 (the stock price at the end of the back test period), R1=$1423.17 (the

first rung level), R2=$1265.17 (the second rung level) and K=$1581.30 (ATMF on the end

date of the back test period). Substituting in the appropriate values:

{ }

The lowest rung level was hit but the final stock price is less than this, thus:

Leg 1 -$ Leg 1 324$

Leg 2 158$ Leg 2 -$

Leg 3 158$ Leg 3 -$

Leg 4 -158 $ Leg 4 -$

Leg 5 -158 $ Leg 5 -$

2RLC Leg Payoff-$

2RLP Leg Payoff324$

2-Rung Ladder Put Replicating Portfolio : Vanilla & Down-and-

Out Calls

2-Rung Ladder Call Replicating Portfolio : Vanilla & Down-

and-Out Puts

Vanilla Put (K=F)

Vanilla Call Spread (F,R1)

Vanilla Call Spread (R1,R2)

Knock-Out Call Spread (F,R1)

Knock-Out Call Spread (R1,R2)

Vanilla Call (K=F)

Vanilla Put Spread (F,R1)

Vanilla Put Spread (R1,R2)

Knock-Out Put Spread (F,R1)

Knock-Out Put Spread (R1,R2)

Constituent Payoffs at

MaturityLeg Description



Implemented Replicating Portfolio

2 Rung Ladder Forward

Combined Payoff:

$324

323.70

Table 8: Summary of Long Ladder Forward over Backtest Period

This is confirms the 2RLP payoff demonstrated in Figure 28.

2.7 Ladder Forward Replicating Portfolio Benchmarking:

In order to provide further intuition and validation with regard the payoffs from the Long

Ladder Forward structured investment product, the constituent payoffs are analyzed over the

back-test period in Appendix 2.

For a thorough analysis, both the implemented replicating portfolio and an alternative

replicating portfolio were constructed and constituent payoffs benchmarked against the

Bloomberg OSA equivalents. The components and payoffs attributed to the alternative

replicating portfolio are summarized in Table 9.

Table 9: Summary of constituent payoffs attributed to Alternative Replicating Portfolio

Leg 1-$

Leg 1158$

Leg 2-$

Leg 2158$

Leg 3-$

Leg 37$

2RLC Leg Payoff-$

2RLP Leg Payoff324$

Alternative Replicating Portfolio (Validation)

2-Rung Ladder Put Replicating Portfolio : Vanilla & Down-and-Out

Puts with Rebates

2-Rung Ladder Call Replicating Portfolio : Vanilla & Up-and-Out

Calls with Rebates

ATMF Strike Up-and-Out Call :

Knocks-out at R1 with 10% Rebate

R1 Strike Up-and-Out Call :

Knocks-out at R2 with further 10% Rebate

R2 Strike Vanilla Call

R1 Strike Down-and-Out Put :


R2 Strike Vanilla Put

$324






Combined Payoff:

ATMF Strike Down-and-Out Put :


2.8 Risk-return Tradeoff Analysis – Downside Capital Loss Protection:

In order to incorporate low cost capital protection into the ladder forward structured

investment product, a collar was created by combining a sold call option and a bought put

option. The sold call option acts as a ‘cap’ and the bought put acts as a ‘floor’. Figure 29

illustrates the construction of the ‘cap’. The strike price was set as 130% ATMF, i.e.

$2,111.06.

Figure 29: OVME Floor creation Figure 30: OVME Cap creation

Additionally, Figure 30 illustrates the bought put, acting at the ‘floor’. The strike price was

set to 70% ATMF, i.e. $1,136.71. The ‘cap’ and ‘floor’ were combined with the existing long

ladder forward and the resulting pay off profile is illustrated in Figure 31. The corresponding

rung levels are indicated in Figure 31, as the kinks in the near dated pay off (yellow) line,

while the cap and floor are demonstrated in the green line.

Figure 31: Payoff profile of financially engineered collar investment product

2.9 Collar Backtest over 01/01/2008 – 12/31/2011:

Illustrated in Figure 32 is the SPX over the pay off period of 01/01/2008-12/31/2011. The

lower rung levels of the 2RLP are illustrated, along with the floor level of the collar, i.e.

1,106.91. The ‘cap’ and ‘floor’ were back tested in OSA.

Figure 32: SPX over backtest period with 2RLP rung levels and Floor

Figure 33 illustrates the ‘cap’, with the expiry date set end of the back testing period, and the

cap level set to 130% of the ATMF price at the end of the expiry date, i.e. $2,055.69.

Additionally, Figure 34 illustrates the ‘floor’, with the expiry date set end of the back testing

period, and the cap level set to 70% of the ATMF price at the end of the expiry date, i.e.

$1,106.91.

Figure 33: OVME Floor back-test Figure 34: OVME Cap back-test

The corresponding pay-off for the call option (cap) is as follows:

The stock price is equal to the final stock price at the end of the back-test period ( ), while the strike price is equal ‘cap’ level ( ). Thus the pay-off

follows:

This is confirms the market price in Figure 35 for the cap pay-off. The corresponding pay-off

for the put option (floor) is as follows:

The stock price is equal to the final stock price at the end of the back-test period ( ), while the strike price is equal ‘floor’ level ( ). Thus the pay-off

follows:

This is confirms the market price in Figure 35 for the cap pay-off.

Figure 35: Collar backtest in OSA

For additional validation, these backtests were conducted and summarised in Appendix 3.

Autocall Barrier 105% YearTrading

Days

Cumulative

Trading Days

Last Day of

TradeMin {St} Max {St}

Lower Protection Barrier 55% 2008 253 253 31/12/2008 46.75 101.3

Knock-In Put Conventional Strike 100% 2009 252 505 31/12/2009

Y5 Knock-Out Barrier 0% 2010 252 757 31/12/2010

2011 252 1009 30/12/2011

2012 250 1259 31/12/2012

Year 2008 2009 2010 2011 2012

Trading Days 253 252 252 252 250

S(t) (Normalised) 62.4 77.1 86.9 86.9 98.69

Component C(t) 10% 20% 30% 40% 50%

+0%/105% Put w/ n*C% cash rebate Coupons - - - - -

+0%/105% Put w/ FV=100% cash rebate Early Redemption - - - -

+0%/0% Put w/ FV=100% cash rebate Final Redemption 100

-100%/50% Knock-In Put KI Put P&L 1.31-

Total Payment - - - - 98.69

Autocallable Payoff Profile per Year

Payoff Calculations for Autocallable Structured Investment Product

Autocallable: Input Variables SPX Trading Days 2008-2012 SPX Price

Bloomberg

Payoff

Validated

40

50

60

70

80

90

100

110

2008 2009 2010 2011 2012

SPX

Pric

e (N

orm

alis

ed)

Autocallable Backtest Period 2008-2011

Protection Barrier

Autocall Barrier

SPX Price (Normalised)

Appendix 1: Payoff Calculations for Autocallable Note Structured Investment Product

S(0) S(T) Max(St) K / F S(0) S(T) Min(St) K / F

$1,447 $1,258 $1,447 $1,581 $1,739 $1,898 $1,447 $1,258 $677 $1,581 $1,423 $1,265

Leg 1 -$ - Leg 1 324$

Leg 2 158$ Leg 2 -$

Leg 3 158$ Leg 3 -$

Leg 4 -158 $ Leg 4 -$

Leg 5 -158 $ Leg 5 -$

2RLC Leg Payoff-$

2RLP Leg Payoff324$

Leg 1-$

Leg 1158$

Leg 2-$

Leg 2158$

Leg 3-$

Leg 37$

2RLC Leg Payoff-$

2RLP Leg Payoff324$ $324

Payoff Calculations for European-exercise ATM 2-Rung Ladder Call and Ladder Put Options










Combined Payoff:

2-Rung Ladder Call: Input Variables



Implemented Replicating Portfolio


Combined Payoff:

$324









Vanilla Put (K=F)

Alternative Replicating Portfolio (Validation)

2-Rung Ladder Put Replicating Portfolio : Vanilla & Down-and-Out

Puts with Rebates

2-Rung Ladder Call Replicating Portfolio : Vanilla & Up-and-Out

Calls with Rebates




Knock-Out Call Spread (R1,R2)

Vanilla Call (K=F)


Vanilla Put Spread (R1,R2)

Knock-Out Put Spread (F,R1)

Knock-Out Put Spread (R1,R2)

2-Rung Ladder Put: Input Variables

2-Rung Ladder Put Replicating Portfolio : Vanilla & Down-and-

Out Calls

2-Rung Ladder Call Replicating Portfolio : Vanilla & Down-

and-Out Puts

650

850

1050

1250

1450

1650

1850

2050

02

/01

/20

08

02

/02

/20

08

02

/03

/20

08

02

/04

/20

08

02

/05

/20

08

02

/06

/20

08

02

/07

/20

08

02

/08

/20

08

02

/09

/20

08

02

/10

/20

08

02

/11

/20

08

02

/12

/20

08

02

/01

/20

09

02

/02

/20

09

02

/03

/20

09

02

/04

/20

09

02

/05

/20

09

02

/06

/20

09

02

/07

/20

09

02

/08

/20

09

02

/09

/20

09

02

/10

/20

09

02

/11

/20

09

02

/12

/20

09

02

/01

/20

10

02

/02

/20

10

02

/03

/20

10

02

/04

/20

10

02

/05

/20

10

02

/06

/20

10

02

/07

/20

10

02

/08

/20

10

02

/09

/20

10

02

/10

/20

10

02

/11

/20

10

02

/12

/20

10

02

/01

/20

11

02

/02

/20

11

02

/03

/20

11

02

/04

/20

11

02

/05

/20

11

02

/06

/20

11

02

/07

/20

11

02

/08

/20

11

02

/09

/20

11

02

/10

/20

11

02

/11

/20

11

02

/12

/20

11

SPX

LP

rice

Long Ladder Forward Backtest Period 2008-2011

SPX Price

Rung 1 Call

Rung 2 Call

Rung 1 Put

Rung 2 Put

ATMF Baseline

Bloomberg

Payoffs Validated

Appendix 2: Payoff Calculations for Long Ladder Forward

S(0) S(T) Max(St) K / F Cap Strike S(0) S(T) Min(St) K / F Floor Strike

$1,447 $1,258 $1,447 $1,581 $1,739 $1,898 $2,056 $1,447 $1,258 $677 $1,581 $1,423 $1,265 $1,107

Leg 1 -$ Leg 1 324$

Leg 2 158$ Leg 2 -$

Leg 3 158$ Leg 3 -$ Leg 4 -158 $ Leg 4 -$ Leg 5 -158 $ Leg 5 -$ Leg 6 -$ Leg 6 -$

2RLC Leg

Payoff -$ $3242RLP Leg

Payoff 324$

Leg 1-$

Leg 1158$

Leg 2-$

Leg 2158$

Leg 3 -$ Leg 3 7$

Leg 4 -$ Leg 4 -$ 2RLC

Capped Leg

Payoff-$ $324

2RLP

Floored Leg

Payoff324$

2-Rung Ladder Capped Call Replicating Portfolio :

Vanilla & Down-and-Out Puts


with Cap & Floor

Combined Payoff:




Constituent Payoffs

at Maturity

Constituent Payoffs

at MaturityLeg Description



2-Rung Ladder Call: Input Variables

Payoff Calculations for European-exercise ATM 2-Rung Ladder Capped Call and Ladder Floored Put Options




Constituent Payoffs

at Maturity

Constituent Payoffs

at MaturityLeg Description

Vanilla Call (K=F)

2-Rung Ladder Put: Input Variables

Leg Description

2-Rung Ladder Floored Put Replicating Portfolio :

Vanilla & Down-and-Out Calls

Implemented Replicating Portfolio - Including Protection

Vanilla Put (K=F)





Leg Description


Vanilla Put Spread (R1,R2)Knock-Out Put Spread (F,R1)

Knock-Out Put Spread (R1,R2)Short Vanilla Call (K=F*130%)

Knock-Out Call Spread (R1,R2)Long Vanilla Put (K=F*70%)


with Cap & Floor

Combined Payoff:

2-Rung Ladder Protected Put Replicating Portfolio : Vanilla &

Down-and-Out Puts with Rebates

Alternative Replicating Portfolio - Including Protection (Validation)

2-Rung Ladder Capped Call Replicating Portfolio : Vanilla &

Up-and-Out Calls with Rebates

Short Vanilla Call (K=F*130%) Long Vanilla Put (K=F*70%)


650

850

1050

1250

1450

1650

1850

2050

2250

02/0

1/20

08

02/0

2/20

08

02/0

3/20

08

02/0

4/20

08

02/0

5/20

08

02/0

6/20

08

02/0

7/20

08

02/0

8/20

08

02/0

9/20

08

02/1

0/20

08

02/1

1/20

08

02/1

2/20

08

02/0

1/20

09

02/0

2/20

09

02/0

3/20

09

02/0

4/20

09

02/0

5/20

09

02/0

6/20

09

02/0

7/20

09

02/0

8/20

09

02/0

9/20

09

02/1

0/20

09

02/1

1/20

09

02/1

2/20

09

02/0

1/20

10

02/0

2/20

10

02/0

3/20

10

02/0

4/20

10

02/0

5/20

10

02/0

6/20

10

02/0

7/20

10

02/0

8/20

10

02/0

9/20

10

02/1

0/20

10

02/1

1/20

10

02/1

2/20

10

02/0

1/20

11

02/0

2/20

11

02/0

3/20

11

02/0

4/20

11

02/0

5/20

11

02/0

6/20

11

02/0

7/20

11

02/0

8/20

11

02/0

9/20

11

02/1

0/20

11

02/1

1/20

11

02/1

2/20

11

SPX

LPric

e

Long Ladder Forward Backtest Period 2008-2011

SPX Price

Rung 1 Call

Rung 2 Call

Rung 1 Put

Rung 2 Put

ATMF Baseline

Cap

Floor

Bloomberg

Payoffs Validated

Appendix 3: Payoff Calculations for Long Ladder Forward with Cap and Floor

Bear Market Flat Market Bull Market0

100

200

300

400

500

600

700

800

900

1000Distribution of Payoff Probabilities for 5Y Autocallable Note

Market Scenarios

Pro

bab

ilit

y %








Bull Market Upturn Flat Market Downturn Bear Market0

10

20

30

40

50

60

70

80

90

100Distribution of Payoff Probabilities for Long Ladder Forward

Pro

bab

ilit

y %

Market Scenarios

20% Gain

10% Gain

Surplus

Deficit

10% Loss

20% Loss

Appendix 4: Marketing Brochure for Auto-callable and Long Ladder Forward

Structured Investment Products

Appendix 5: Matlab Code

Bibliography

Citigroup, 2007. Autocallable Overview, New York: Citigroup.

Dash, S. & Moran, M. T., 2005. VIX as a Companion for Hedge Fund Portfolios. The

Journal of Alternative Investments, September, 8(3), pp. 75-80.

Dow, J., Ribeiro, S. & Werlang, C., 1992. Uncertainty aversion, risk aversion, and the

optimal choice of portfolio. Econometrica: Journal of the Econometric Society, pp. 197-204.

Glosten, L., Jagannathan, R. & Runkle, D., 1993. On the relation between the expected value

and the volatility of the nominal excess return on stocks. The journal of finance, 5(48), pp.

1779-1801.

Heston, S., 1993. A closed-form solution for options with stochastic volatility with

applications to bond and currency options.. Review of Financial Studies, 6(2), pp. 327-343.

McCann, C., 2006. Are Structured Products Suitable for Retail Investors?. [Online]

Available at: http://www.slcg.com/pdf/workingpapers/StructuredProducts.pdf

[Accessed 10 April 2015].

Murphy, B., 2015. Financial Engineering - Autocallable Replicating Portfolio Eurostoxx50

5Y Backtest 2007-2011. [Online]

Available at: https://sulis.ul.ie/access/content/attachment/ba0a90ab-161d-440d-979f-

42a51da03df8/Announcements/625c5035-6418-40c2-8039-

3e54efff955a/Autocallable%20Replicating%20Portfolio%20Eurostoxx50%205Y%20Backtes

t%202007-2011.xlsx

Murphy, B., 2015. Lecture Week 7. s.l.:s.n.

Murphy, B., 2015. Week 7 Lecture Materials. [Online]

Available at: https://sulis.ul.ie/xsl-portal/site/ba0a90ab-161d-440d-979f-

42a51da03df8/page/07ea5598-281f-4e58-b66d-35f2110b1c0b

[Accessed 8 March 2015].

National Association of Securities Dealers, 2005. Notice to Members 05-26. [Online]

Available at: https://www.finra.org/sites/default/files/NoticeDocument/p013755.pdf

[Accessed 10 April 2015].

structured investment product - construction, backtesting and analysis

Documents

autocallable note creation

autocallable note benchmark

autocallable note conclusion

long ladder

short ladder

evan ryan

payoff calculations

barry sheehan title