הנדסה פיננסית

2003 1

הנדסה פיננסית

צבי וינר

[email protected]

02-588-3049

הנדסה פיננסיתhttp://pluto.huji.ac.il/~mswiener/zvi.html 2

השקעות בסיסיות

מניות• אגחים + הלוואות• מטבעות• סחורות• נדל"ן•


נגזרות פיננסיות

אופציות בסיסיות•(Forwards and Futures) חוזים עתידיים •(Swaps) סוופים • אופציות אקזוטיות•(structured products) סטרקצ'ורים •


אופציה רכש אירופית

אופציה

Kנכס בסיס

(0,) KSMax


אופציה

K

אופציית מכר אירופית

Kנכס בסיס

(0,) SKMax

2003 6

אופציות ברירה

צבי וינר

[email protected]

02-588-3049


אופציית ברירה

₪ היום ומקבל בסוף שנה את 100לקוח מפקיד המקסימום בין הצמדה לדולר + ריבית דולרית לבין

ריבית אירו. הצמדה לאירו +

איך הבנק צריך לגדר את התוכנית?


אופציית ברירהנגדיר:

t Atשער הדולר ביום

tBtשער האירו ביום

RAריבית דולרית מובטחת

RBריבית אירו מובטחת

QAכמות דולרים מובטחת

QBכמות אירו מובטחת


אופציית ברירה

TAA R

AQ (1)

100

0

TBB R

BQ (1)

100

0


תשלום מובטח בפדיון

BTAT QBQAMax ,

B

T

TA QA

BQMax ,

משקיע אמריקאי


B

T

TA QA

BQMax ,

AB

T

TA QQ

A

BMaxQ ,0

B

A

T

TBA Q

Q

A

BMaxQQ ,0


B

A

T

TBA Q

Q

A

BMaxQQ ,0

תשלום בפדיון בדולרים

B

A

T

TBtT

A

A

Q

QK

A

BSCallQ

r

Q,

(1)

שווי היום בדולרים


שווי היום בדולרים

B

A

T

TtBtT

A

tA

Q

QK

A

BSCallAQ

r

AQ,

(1)

שווי היום בשקלים

B

A

T

TBtT

A

A

Q

QK

A

BSCallQ

r

Q,

(1)

()() 12 dNeBQdNeAQ BA rtB

rtA


ברירה עם משקולותX, Yשני מסלולים

כאשר התשלום הסופי מחושב לפי

(,)(1)(,) YXMinYXMax

לדוגמה

.3% אן צמוד מדד + 1% צמוד דולר + מסלולים:

התשלום

של המסלול הטוב ביותר,70%

של המסלול הפחות טוב.30%פלוס


ברירה עם משקולות

(,)3.0(,)7.0 YXMinYXMax

(,)4.0()3.0 YXMaxYX

YXXYXYX 3.07.04.0()3.0,

XYYYXXY 3.07.04.0()3.0,


Currency Options

Standard 1 year investments

2.5% linked to USD

3.5% linked to EUR

Option A: you get maximum of

0.5% linked to USD or

1.5% linked to EUR

Option B: you get minimum of

5.0% linked to USD or

6.5% linked to EUR.


Source: J. Siegel, )IRWIN(


Standard Investments

Stock

S

Bond1+r

1

1Probability distribution

value


Portfolio 50-50

50% Stock

S

50% Bond

2

1 r

50-50 portfolio

Trade off

value


Various Portfolios

S

50-50 portfolio

5.0(1) r

1 1+r

(1) r 100-0 portfolio

7.0(1) r

70-30 portfolio

Probability distribution

value


VITUR

S

R1

K

pricing

value


Collar

SKF KC

F

C

value


Examples

NDX

$

100

100

166

70%100%


TA-25, 3 years VITUR )example(

TA25

R1

K

VITUR

Floor VITUR0% 40%5% 50%9% 60%12% 70%

value


TA-25, 3 years VITUR )example(

TA25

value

Linear strategy

VITUR

1.08


TA 25, 3 years collar example

TA25KF KC

F

C

F

C

Floor Cap0% 50%5% 40%9% 35%12% 30%

value


Tailored Loan with Collateral

Firm B has shares of firm C of value $100M.

They do not want to sell the shares, but need

money )70-90M for 3 years(.

Moreover, they would like to decrease the

exposure to financial risk.

How can it be done?


Collarצווארון = payoff

90 100 K

90

K

מניה


Collarצווארון = payoff

90 100 K

90

K

מניה

הלוואה זולה


S90%

160-170%

100%

Collarצווארון = 90%, ריצפה 6%שנים, ריבית 3

= 10%, cap )K( = 62%

= 20%, cap )K( = 69%

= 30%, cap )K( = 77%


Swaps

Exchange of cashflows:

IR swaps

currency swaps

Amortizing swaps

Total return swaps

Credit default swaps

Asset swaps


Global Derivatives Markets 1999

IR contracts 60,091FRAs 6,775Swaps 43,936Options 9,380FX contracts 14,344Forwards 9,593Swaps 2,444Options 2,307Equity-linked contr. 1,809Forw. and swaps 283Options 1,527Commodity contr. 548Others 11,408

OTC Instruments $88TExchange traded $13.5TIR contracts 11,669Futures 7,914Options 3,756FX contracts 59Futures 37 Options 22Stock-index contr. 1,793Futures 334Options 1,459

Source BIS

World GDP in 99 = 30,000BAll stocks and bonds = 70,000Liquidation value = 2,800B


Global Derivatives Markets 2001

IR contracts 77,513FRAs 7,737Swaps 58,897Options 10,879FX contracts 16,748Forwards 10,336Swaps 3,942Options 2,470Equity-linked contr. 1,881Forw. and swaps 320Options 1,561Commodity contr. 598Others 14,375

OTC Instruments $111TExchange traded $23.5TIR contracts 21,614Futures 9,137Options 12,477FX contracts 89Futures 66 Options 23Stock-index contr. 1,838Futures 295Options 1,543

Source BIS


Interest Rate Swaps: Concept

• An agreement between 2 parties to exchange periodic payments calculated on the basis of specified interest rates and a notional amount.

•Plain Vanilla Swap

A BFixed rate

Floating rate

Based on a presentation of Global Risk Strategy Group of Deutsche Bank


IRS• In a standard IRS, one leg consists of fixed rate payments and the other depends on the evolution of a floating rate.• Typically long dated contracts: 2-30 years• Sometimes includes options, amortization, etc.• Interest compounded according to different conventions )eg 30/360, Act/Act. Act/360, etc.(


IRS OriginsAAA wants to borrow in floating and BBB wants to borrow in fixed.

Fixed Floating

AAA 7.00% LIBOR+5bps

BBB 8.50% LIBOR+85bps

difference 1.5% 0.8%

Net differential 70bps = 0.7%


Comparative Advantage

Cost of funds for AAA=Libor - 40bp )45bps saved(

Cost of funds for BBB=8.25% )25bps saved(

Swap rate = 7.40%

Swap rate is the fixed rate which is paid against receiving Libor.

AAA BBBLibor

7.4%7.0% Libor+85bp


Reverse Floater

USD 5 year interest rates are 5%, however short

term interest rates are Libor =2%.

Libor = London Interbank offered rate

on Bloomberg see FWCV + currency

One can construct so-called reverse floater:


Reverse Floater

Years

0

1

2

3

4

5

bond

-100

5

5

5

5

105

loan

+100

-L0

-L1

-L2

-L3

-100- L4

Reverse Fl.

-100

8

10-L1

10-L2

10-L3

110- L4

bond

-100

5

5

5

5

105


Callable Principal Protected Note

• SP500 )monthly average of the 5th year(

• Maturity 5 years

• Floor 100% in USD terms

• Profit participation 100%

• Callable at 110%, 120%, 130%, 140%

• Probability to be called above 80%


Periodic Cap + Global Floor• 3 year contract• guaranteed return to the investment )e.g. 110%(• linkage to a liquid index )e. g. S&P, TA-25(• average of capped quarterly returns is the upside )e.g. 8%(• very high upside )96% in the example( with guaranteed profit

2003 42

Non-recourse loan

צבי וינר

[email protected]

02-588-3049


Non-recourse loan

A loan with collateral but NO residual claims!

This means that at worst one can take the

collateral but no other assets can be used to

fulfill the original schedule.


Non-recourse loan

collateral

Payoff to borrower

)1+R(T

)1+R(T


Non-recourse subordinated loan

collateral

Payoff

debt

debt

Loan 1

Loan 2


Basic Structures• Step up bonds• Principal protected notes• Callable structures• Equity linked notes• Ranges• Quantos• CDO• Swaps )FX, IR, credit(


Risks• Business Risk• Financial Risk

– market risk– credit risk– liquidity risk

• Operational Risk– technology– people– external events

• Legal Risk

Measure

Protect Measure

Protect

2003 48

ESOP

צבי וינר

[email protected]

02-588-3049


Long term options

payoff

k K stock

50

K

Sell a call

Your option

Result


ExampleYou have 10,000 vested options for 10 years

with strike $5, while the stock is traded at $10.

An immediate exercise will give you $50,000

before tax.

Selling a )covered( call with strike $15 will

give you $60,000 now )assuming interest rate

6% and 50% volatility( and additional profit at

the end of the period!


Example

payoff

10 15 26

50

K

Your option

Result

60

exercise

הנדסה פיננסית

Documents

libor 85bpsdifference1

libor 5bpsbbb8

floating rate

fixed rate payments

savedswap rate

source bisinterest rate

fx contracts16

fx contracts14