- 1 - topic 4: derivative securities in global financial markets purpose: provide background on the...
TRANSCRIPT
- 1 -
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
- 3 -
Derivatives
• Swaps – Futures and Forward Contracts On Swaps
• Options – Currency Options – Swaptions – Options On Futures – Futures On Options
- 4 -
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
- 5 -
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
- 6 -
The basics of options
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
- 7 -
The basics of options
• 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
- 8 -
Binomial Approach
- 9 -
- 10 -
DCF only
Augmented
- 11 -
- 12 -
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
- 13 -
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
- 14 -
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)
- 15 -
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)
- 16 -
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
- 17 -
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)
- 18 -
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)
- 19 -
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
- 20 -
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)
- 21 -
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)
- 22 -
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)
- 23 -
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)
- 24 -
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)
- 25 -
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)
- 26 -
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)
- 27 -
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)
- 28 -
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)
- 29 -
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)
- 30 -
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)
- 31 -
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)
- 32 -
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
- 43 -
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)
- 44 -
Basic Option Strategies
• Long Call
• Long Put
• Short Call
• Short Put
• Long Straddle
• Short Straddle
• Box Spread
- 45 -
Long Call
S
$
0
- CX
X+C
- 46 -
Short Call
S
$
0
- CX
X+CLon
g C
all
XS
$
0X+CC
- 47 -
Long Put
S
$
0
- CX
X+CX
S
$
0X+CC
Lon
g C
all
Sho
rt C
all
S
$
0X
- P
X-P
- 48 -
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
- 49 -
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
- 50 -
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
- 51 -
Box Spread
• Long call, short put, exercise = X• Same as buying a futures contract at X
SX
$
0
- 52 -
Box Spread
• Long call, short put, exercise = X• Short call, long put, exercise = Z
SX
$
0Z
- 53 -
Box Spread
• You have bought a futures contract at X• And sold a futures contract at Z
SX
$
0Z
- 54 -
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
- 55 -
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
- 56 -
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
- 57 -
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
- 58 -
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
- 59 -
Currency Options
Options to exchange one currency for another
- 60 -
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
- 61 -
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
- 62 -
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
- 63 -
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
- 64 -
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
- 65 -
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
- 77 -
- 78 -
Swaps
- 79 -
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
- 80 -
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
- 81 -
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
- 82 -
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
- 83 -
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
- 85 -
Equity Call Swap
Investor Underwriter
Illustration of an Equity Call Swap
Equity Index Price Appreciation*
* No depreciation—settlement at maturity
Libor ± Spread
- 86 -
Equity Asset Swap
Underwriter
Equity Index Return*
* Equity index return includes dividends, paid quarterly or reinvested
Income Stream
Investor
Income
Stream
Asset
- 87 -
Bringing these innovations to the retail level
- 88 -
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
Investor Underwriter
Illustration of an Equity Call Swap
Equity Index Price Appreciation*
* No depreciation—settlement at maturity
Libor ± Spread
- 90 -
- 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
- 92 -
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
- 93 -
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
- 94 -
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