- 1 - topic 4: derivative securities in global financial markets purpose: provide background on the...

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Topic 4: Derivative Securities in Global Financial Markets

Purpose:• Provide background on the basics of Option

Pricing Theory (OPT) • Examine some recent applications of

derivatives in international finance

- 2 -

Derivatives

Derivative = obligation to accomplish a transaction in the future

Forward Contract = basic derivative from which all others have evolved

• Repurchase Agreements – Reverse Repurchase Agreements

• Futures Contracts

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Derivatives

• Swaps – Futures and Forward Contracts On Swaps

• Options – Currency Options – Swaptions – Options On Futures – Futures On Options

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What are options?

• Options are financial contracts whose value is contingent upon the value of some underlying asset

• Such arrangements are also known as contingent claims– because equilibrium market value of an option

moves in direct association with the market value of its underlying asset.

• OPT measures this linkage

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The basics of options

Calls and puts defined

• Call: privilege of buying the underlying asset at a specified price and time

• Put: privilege of selling the underlying asset at a specified price and time

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Regional differences

• American options can be exercised anytime before expiration date

• European options can be exercised only on the expiration date

• Asian options are settled based on average price of underlying asset

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• Options may be allowed to expire without exercising them

• Options game has a long history– at least as old as the “premium game” of

17th century Amsterdam– developed from an even older “time game”

• which evolved into modern futures markets

• and spawned modern central banks

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Binomial Approach

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DCF only

Augmented

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As the binomial change process runs faster and faster, it approaches something known as Brownian Motion

Let’s have a sneak preview of the Black-Scholes model, using a

similar example

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Illustration using Black-Scholes

Value of 1st year’s option = $1135.45

Value of 2nd year’s option = $1287.59

NPV = –2000 + 1135.40 + 1287.59 = $423.04

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Put-Call Parity

Consider two portfolios

• Portfolio A contains a call and a bond:

C(S,X,t) + B(X,t)

• Portfolio B contains stock plus put:

S + P(S,X,t)

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Put-Call Parity

Consider two portfolios

• Portfolio A contains a call and a bond:

C(S,X,t) + B(X,t)

• Portfolio B contains stock plus put:

S + P(S,X,t)

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Put-Call Parity

C(S,X,t) + B(X,t) = S + P(S,X,t)

• News leaks about negative event• Informed traders sell calls and buy puts

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Put-Call Parity

• News leaks about negative event• Informed traders sell calls and buy puts• Arbitrage traders buy the low side and sell the

high side

C(S,X,t) + B(X,t) = S + P(S,X,t)

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Put-Call Parity

• News leaks about negative event• Informed traders sell calls and buy puts• Arbitrage traders buy the low side and sell the

high side• Stock price falls — “the tail wags the dog”

C(S,X,t) + B(X,t) = S + P(S,X,t)

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Boundaries on call values C(S,X,t) + B(X,t) = S + P(S,X,t)C(S,X,t) + B(X,t) = S + P(S,X,t)

• Upper Bound:C(S,X,t) < S

Stock

Cal

l

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Boundaries on call values C(S,X,t) + B(X,t) = S + P(S,X,t)C(S,X,t) + B(X,t) = S + P(S,X,t)

• Upper Bound:C(S,X,t) < S

• Lower bound: C(S,X,t) ≥ S – B(X,t)

Stock

Cal

lB(X,t)

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Call values C(S,X,t) = S - B(X,t) + P(S,X,t)C(S,X,t) = S - B(X,t) + P(S,X,t)

Stock

Cal

l

B(X,t)

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Stock

Cal

l

B(X,t)

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Stock

Cal

l

B(X,t)

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Stock

Cal

l

B(X,t)

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Stock

Cal

l

B(X,t)

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Stock

Cal

l

B(X,t)

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Stock

Cal

l

B(X,t)

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Stock

Cal

l

B(X,t)

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Stock

Cal

l

B(X,t)

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Stock

Cal

l

B(X,t)

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Stock

Cal

l

B(X,t)

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Keys for using OPT as an analytical tool C(S,X,t) = S - B(X,t) + P(S,X,t)C(S,X,t) = S - B(X,t) + P(S,X,t)

Stock

Cal

l

B(X,t) Stock

Cal

l

B(X,t)

S C

X C

t C

C

R C

P

P

P

P

P

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Impact of Limited Liability C(V,D,t) = V - B(D,t) + P(V,D,t)

B(D,t) V

Equ

ity

• Equity = C(V,D,t)• Debt = V - C(V,D,t)

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Basic Option Strategies

• Long Call

• Long Put

• Short Call

• Short Put

• Long Straddle

• Short Straddle

• Box Spread

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Long Call

S

$

0

- CX

X+C

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Short Call

S

$

0

- CX

X+CLon

g C

all

XS

$

0X+CC

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Long Put

S

$

0

- CX

X+CX

S

$

0X+CC

Lon

g C

all

Sho

rt C

all

S

$

0X

- P

X-P

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Short Put

S

$

0

- CX

X+CX

S

$

0X+CC

Lon

g P

utL

ong

Cal

l

Sho

rt C

all

S

$

0X

- P

X-P

S

$

0

P

XX-P

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Long Straddle

S

$

0

- CX

X+CX

S

$

0X+CC

Lon

g P

utL

ong

Cal

l

Sho

rt C

all

S

$

0

P

XX-P

S

$

0X

- P

X-P

Sho

rt P

ut

S

$

0X

-(P+C)

X-P-C

X+P+C

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Short Straddle

S

$

0

- CX

X+CX

S

$

0X+CC

Lon

g P

utL

ong

Cal

l

Sho

rt C

all

S

$

0

P

XX-P

S

$

0X

- P

X-P

Sho

rt P

ut

S

$

0X

-(P+C)

X-P-C

X+P+C

Lon

gS

trad

dle $

0X

P+C

X-P-C

X+P+C

S

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Box Spread

• Long call, short put, exercise = X• Same as buying a futures contract at X

SX

$

0

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Box Spread

• Long call, short put, exercise = X• Short call, long put, exercise = Z

SX

$

0Z

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Box Spread

• You have bought a futures contract at X• And sold a futures contract at Z

SX

$

0Z

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Box Spread• Regardless of stock price at expiration

– you’ll buy for X, sell for Z– net outcome is Z - X

SX

$

0Z

Z - X

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Box Spread• How much did you receive at the outset?

+ C(S,Z,t) - P(S,Z,t)- C(S,X,t) + P(S,X,t)

SX

$

0Z

Z - X

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Box SpreadBecause of Put/Call Parity, we know:

C(S,Z,t) - P(S,Z,t) = S - B(Z,t)- C(S,X,t) + P(S,X,t) = B(X,t) - S

SX

$

0Z

Z - X

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Box Spread• So, building the box brings you

S - B(Z,t) + B(X,t) - S = B(X,t) - B(Z,t)

SX

$

0Z

Z - X

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Assessment of the Box Spread

• At time zero, receive PV of X-Z• At expiration, pay Z-X• You have borrowed at the T-bill rate.

SX

$

0Z

Z - X

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Currency Options

Options to exchange one currency for another

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The basics of currency options

• Call: privilege of buying the underlying currency at a specified exchange rate and time– A call option written on the U.S. Dollar in London, for example, gives the

holder the privilege (but not the obligation) of buying U.S. Dollars in exchange for British Pounds at a specified exchange rate

• Put: privilege of selling the underlying currency at a specified exchange rate and time– a put option written on the Pound in New York conveys the privilege of

selling Pounds in exchange for Dollars at a specified rate

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The basics of currency options

• Call: privilege of buying the underlying currency at a specified exchange rate and time

• Put: privilege of selling the underlying currency at a specified exchange rate and time

• The twist is that the put option written in New York is the same thing as the call option written in London, when both have the same expiration date– Any disparity in prices would present a

lucrative but short-lived arbitrage opportunity

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Example of Parity in Currency Options

New York• $5 buys a put to sell

£60 in exchange for $100 (exchange at the forward rate)

London• Find equilibrium

price for a call to buy $100 in exchange for £60 (exchange at the forward rate)

• Answer:$5 * .62 = £3.10

$1 = £0.62 spot$1 = £0.60 forward

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Example of Parity in Currency Options

New York• $5 buys a put to sell

£60 in exchange for $100 (exchange at the forward rate)

London• Find equilibrium

price for a call to buy $200 in exchange for £120 (exchange at the forward rate)

• Answer:$10 * .62 = £6.20

$1 = £0.62 spot$1 = £0.60 forward

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Using Scale to Compare Options

• The previous example gives us insight into the ability to adjust the scale of options:

• The New York involves half as much money as the London option ($100 and £60, compared with $200 and £120)

• We should scale the price of the option accordingly, and find the value of $10 translated into Pounds at the spot exchange rate

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Standardizing Options

• The ability to adjust the scale of options also makes it possible to standardize options for improved comparability in the search for potential arbitrage opportunities:

• Divide the underlying asset’s price by the exercise price, creating an option with an exercise price of one

– Then the value of the underlying asset is adjusted to S/X

• Time and volatility stay the same

• The price of the standardized option will be the old price divided by the exercise price

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Swaps

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Floating-Fixed Swaps

Fixed

If net is positive, underwriter pays party. If net is negative, party pays underwriter.

Illustration of a Floating/Fixed Swap

Party Underwriter CounterpartyVariable

Fixed

Variable

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Floating to Floating Swaps

LIBOR

If net is positive, underwriter pays party. If net is negative, party pays underwriter.

Illustration of a Floating/Floating Swap

Party Underwriter CounterpartyT-Bill

LIBOR

T-Bill

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Parallel Loan

United States Germany

Loan guarantees

Debt service in $

Illustration of a parallel loan

German Parent

U.S. subsidiary of German

Firm

U.S. Parent

German subsidiary of

U.S. Firm

Principal in $

Debt service in Euro

Principal in Euro

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Currency Swap

German rate x €1,000,000

€ 1,000,000

2 2

U.S. rate x $1,500,000

German rate x €1,000,000

U.S. rate x $1,500,000

1 1

€ 1,000,000

$1,500,000$1,500,000

€ 1,000,000

3 3

$1,500,000

€ 1,000,000

$1,500,000

Illustration of a straight currency swap

Step 1 is notionalSteps 2 & 3 are net

Borrow in US, invest in Europe

Borrow in Europe, invest in US

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Swaps

Investor UnderwriterLibor ± Spread

Equity Index Return*

*Equity index return includes dividends, paid quarterly or reinvested

Illustration of an Equity Return Swap

- 84 -

Swaps

Investor Underwriter

Foreign Equity Index Return* A

Illustration of an Equity Asset Allocation Swap

*Equity index return includes dividends, paid quarterly or reinvested

Foreign Equity Index Return* B

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Equity Call Swap


Illustration of an Equity Call Swap

Equity Index Price Appreciation*

* No depreciation—settlement at maturity

Libor ± Spread

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Equity Asset Swap

Underwriter

Equity Index Return*

* Equity index return includes dividends, paid quarterly or reinvested

Income Stream

Investor

Income

Stream

Asset

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Bringing these innovations to the retail level

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PENsS

CP

ER

S

BT

Cou

nte

rpar

y

PE

FC

O

$5 mm

$5mm + Appreciation

1% Coupon Fixed Undisclosed Flow

AppreciationAppreciation

- 89 -

Equity Call Swap


Illustration of an Equity Call Swap

Equity Index Price Appreciation*

* No depreciation—settlement at maturity

Libor ± Spread

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- 91 -

Box Spread• Because of Put/Call Parity, we know:

C(S,Z,t) + B(Z,t) = S + P(S,Z,t)

SX

$

0Z

Z - X

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Box Spread• C(S,Z,t) + B(Z,t) = S + P(S,Z,t)

Now, let’s subtract the bond from each side:• C(S,Z,t) = S + P(S,Z,t) - B(Z,t)

SX

$

0Z

Z - X

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Box Spread• C(S,Z,t) = S + P(S,Z,t) - B(Z,t)

Next, let’s subtract the put from each side:• C(S,Z,t) - P(S,Z,t) = S - B(Z,t)

SX

$

0Z

Z - X

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Box Spread• C(S,Z,t) - P(S,Z,t) = S - B(Z,t)

Given this, we also know:- C(S,X,t) +P(S,X,t) = - S + B(X,t)

SX

$

0Z

Z - X

- 95 -

Box Spread• So, because of Put/Call Parity, we know:

C(S,Z,t) - P(S,Z,t) = S - B(Z,t)

SX

$

0Z

Z - X

- 1 - topic 4: derivative securities in global financial markets purpose: provide background on the...

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