Development of Market for Interest Rate Swaps

1
Development of Market for Interest Rate Swaps

• Increasing standardization
• Fewer one-off deals
• Intermediaries have started taking more risk
• More capital commitment by intermediary
• Intermediaries started hedging risk
• Intermediaries became commercial banks
• Average swap for 25m notional, 3 to 5 years
• Available up to 1b notional, 10 year maturity

2
Growth in Swap Market

• Credit Arbitrage
• Take advantage of a non-zero quality spread
• Quality spread
• Credit spread in fixed rate market - Credit
  spread in variable rate market
• Credit spread
• Yield for low quality issuer - Yield for high
  quality issuer

3
Credit Arbitrage
4
Credit Arbitrage
Net Cost to AAA LIBOR10.8-A
Net Cost to BBB B0.75
Debt (Fixed)
LIBOR 75
10.8
Debt (Floating)
BBB
AAA
B
A
Swap Dealer
LIBOR
LIBOR
5
Credit Arbitrage
For AAA A-10.55 gt 0 or A gt 10.55 For BBB
11.25 - B gt 0 or B lt 11.25 For Swap Dealer A lt B
6
Options
7
Standard Options Definition
A standard call is an option giving the
"buyer" the right to buy from the "seller"
(writer) an "underlying asset" for a fixed
price ("strike price") at any time on or
before a fixed date ("expiration
date"). Terminology
S º current underlying asset price S º
underlying asset price on expiration
date K º strike price of option (exercise
price) t º current time-to-expiration of
option (in years) r º riskless return
(annualized) d º dividend payout return
(annualized) s º underlying asset
volatility C º call value/payoff on
expiration date c º current value/price of a
European call (premium) C º current
value/price of an American call (premium)
8
Standard Options Definitions
A standard put is an option giving the
"buyer" the right to sell to the "seller"
an "underlying asset" for a fixed price
("strike price") at any time on or before
a fixed date ("expiration date"). Terminology

p º current value/price of European put
(premium) P º current value/price of an
American put (premium) P º put value/payoff
on expiration date
Note Exercise styles
European option only exercisable on
expiration date American option
exercisable at any time Bermudan option
exercisable only at some predefined times
Atlantic option exercisable depending on
underlying asset price
9
Buy Call Option
APR/50 call option on CIBC priced at 1.50
Choose to buy 1 share of CIBC at 50 unit (Spot
46.10)
10
Buy Call Option
51.50
11
Write Call Option
Write Jan/45 call on Alcan for 6.50, Stock at
51.50
In exchange for price of call, you promise
to deliver 1 share of Alcan for 45
12
Write Call Option
51.5
13
Buy Put Option
Buy Feb/15 on Air Canada for 3
Choose to sell 1 share of Air Canada for 15
a share (spot price of 12.2)
14
Buy Put Option
12
15
Write Put Option
Write APR/25 put on Barrick Gold for 3, Stock
price is 23
In exchange for the price of the put, you
promise to buy Barrick Gold for 25 per share
16
Write Put Option
22
17
Trading Strategies Involving Options
18
Covered Strategies

• Hedges
• Combine option with stock
• Spreads
• Combine two or more options of same type
• Straddles/Strangles
• Combine call and put
• Strap
• Straddle plus a call
• Strip
• Straddle plus a put

19
Hedges

• Covered Call
• Buy stock, write call
• Protective Put
• Buy stock, buy put
• Protected Short
• Short stock, buy call
• Ratio Hedges
• of options ? of shares of stock

20
Covered Call
You bought 1 share of Celestica for 75, Price now
is 91.3 You write 1 MAR/100 call for 7.05
21
Covered Call
Buy Stock
67.95
107.05
Sell Call
75
Covered Call
22
Protective Put
You bought 1 share of Sun Life at 35, buy
April/40 put at 7
23
Protective Put
Buy Put
Protective Put
Buy Stock
24
Protected Short
You shorted 1 share of JDS Uniphase for 85, buy 1
MAY/70 call for 21
25
Protected Short
Short Stock
Protected Short
Buy Call
26
Ratio Hedge - Calls
Buy 1 share of Nortel for 60, Write 3 MAR/60
calls for 3 each (13 ratio hedge)
27
Ratio Hedge With Calls
Sell 3 calls
Ratio Hedge
Buy stock
28
Ratio Hedge - Puts
Buy 5 shares of RIM at 90, buy 7 Feb/100 puts at
20 (57 ratio hedge)
29
Ratio Hedge With Puts
Puts
55
Ratio Hedge
Stock
118
30
Spreads

• Vertical or Money Spreads
• Options differ in strike
• Horizontal or Time Spreads
• Option differ in maturity
• Diagonal Spreads
• Options differ in strike and maturity

31
Money Spreads

• Bullish spreads
• Buy low strike, write high strike
• Bearish spreads
• Buy high strike, write low strike
• Butterfly spreads
• Combination of bull and bear spreads
• Ratio spreads (Backspreads)
• Buy low strike, write m high strike calls
• Buy high strike, write m low strike puts

32
Bull Spread
Buy 1 MAR/550 put and sell 1 MAR/600 puts on SP
60 Canada Index for 42 and 80
33
Bull Spreads
Buy put
Bull Spread
Sell put
562
34
Bear Spread
Write Apr/20 call on Bombardier for 3.5, Buy
Apr/25 for 1
35
Bear Spread
Buy call
Bear Spread
Sell call
22.5
36
Reverse Butterfly Spread
 
Write Feb/30 and Feb/42 calls on Sun Life, Buy
2 Feb/36 call for 3.6, 0.2 and 1, respectively
37
Reverse Butterfly Spread
36 Call
Reverse Butterfly Spread
42 Call
40.2
31.8
30 Call
38
Top Straddle
Write MAR/80 call and put on Celestica for 17 and
6
39
Top Straddle
Call
57
103
Top Straddle
Put
40
Bottom Strangle
Buy Mar/120 call and Mar/100 put on RIM for 10
and 25
41
Bottom Strangle
Call
Put
Bottom Strangle
42
Other Positions

• Cylinder Buy Call Sell Put (or reverse)
• Collar Underlying Sell call Buy put
• Strap 2 calls put
• Strip 2 puts call
• Condor Bull in-the-money call spread Bear
  out-of-the-money call spread
• Seagull Bull Call Spread Sold Put

43
Basic Properties of Stock Options
44
Factors Affecting Stock Option Prices
European European American
American Variable Call Put
Call Put

• Stock Price (S) -
  -
• Strike Price (K) -
  -
• Volatility (s)
  
• Time to expiration (t) ?
  
• Risk free rate (r) -
  -
• Dividends (d) -
  -

45
Put-Call Parity Relation Numerical Example
with Novell
Underlying Asset Price S 35 Put Price p
7 Strike K 35 Riskless Return r
5.54 Time-to-Expiration t 135
days Current Expiration Date
Date S lt 35 S ? 35
Buy Call - c
0 S - 35 Buy Put
- 7 35 - S
0 Buy 1 unit of Asset - 35
S S
Borrow PV of K 35e-0.0554135/365
- 35 - 35 Total
- 7 - 35 35e-0.0554135/365
0 S - 35 In
general
c 7 35 - 35e0.0554135/365 7.71
c p S - K e-r t
46
Synthetic Call Put Asset BorrowingPayoffs
at expiration
S 35 K 35 t 0.37 r 5.54 d 1.00
47
Put-Call Parity Relation with Dividends
Arbitrage Table
Current
Expiration Date Date S lt K
K ? S Buy Call
- c 0 S - K
Buy Put - p
K - S 0 Buy e -d t
units of Asset - S e -d t S
S Borrow PV of K Ke-r
t - K - K Total
- p - Se -d t K e -r t
0 S - K Note Applies
only to standard European options with known
payouts.
c p S e-d t - K e-r t
48
Early Exercise Calls on Non Dividend Paying Stock

• Lower bound on value of a European call option
• c gt S - K e -r t
• An example
• S 30 r 4 per year, compounded continuously
• Call K 25, c 5.50, t 0.5 yrs
• Strategy?

49
Early Exercise Calls on Non Dividend Paying Stock

• An American option should be more valuable than a
  European option given early exercise potential
• Thus, C ? c
• Since c gt S - K e -r t , it must be that C gt
  S - K e -r t
• For early exercise to be optimal, it must be that
• C ? S - K
• But because interest rates are positive, it must
  also be that
• C gt S - K
• Thus, it never pays to exercise early

50
Early Exercise Puts on Non Dividend Paying Stock

• Lower bound on value of a European put option
• p gt K e -r t - S
• An example
• S 30 r 4 per year, compounded continuously
• Put K 35, p 4.31, t 0.5 yrs
• Strategy?

51
Early Exercise Puts on Non Dividend Paying Stock

• Again, an American option should be more valuable
  than a European option given early exercise
  potential
• Thus, P ? p
• Since p gt K e -r t - S, it must be that P gt K
  e -r t - S
• For early exercise to be optimal, it must be that
• P ? K - S
• This is possible (given the lower bound above),
  especially if S is low, r is high or underlying
  asset return volatility is low

52
Option ValuationBinomial Trees
53
The Binomial Model
Assume that the stock follows a binomial
process Over a time period stock price goes up or
down (ugt1, dlt1)
Su
125
S
100
Sd
80
Consider a call option on this stock that expires
in one period (K100)
cU Max0,125-100 25
c
cD Max0,80-100 0
54
The Hedge Portfolio
Consider a hedge portfolio with 1 share of stock
and aC calls
Su aCcU 12525 aC
S aCc 100 aCc
Sd aCcD 80
Condition 1 Create hedge portfolio so that it is
riskless Su aCcU Sd aCcD or aC
-(u-d)S/(cU-cD) aC -(1.25-0.80)100/25 -1.8
Þ Write 1.8 calls
125(-1.8)(25) 80
100-1.8c
80
55
The Binomial Option Pricing Model

• Condition 2 Riskless hedge portfolio return
  risk-free rate
• In this example, with r 10, t 1
• 100 - 1.8 c 80 e - r t 80 e -0.1 72.387
• 1.8c 27.613
• c15.34

56
Risk Neutral Pricing
Consider a hedge portfolio with 1 share of stock
and aC calls
Su aCcU
S aCc
Sd aCcD
For a hedge portfolio aC -(u-d)S/(cU-cD) Hedge
portfolio generates risk free return S
-(u-d)S/(cU-cD) c Su -(u-d)S/(cU-cD)
cUe-r t
57
Risk Neutral Pricing

• After some considerable algebra
• c p cu (1-p) cd e-r t
• p e r t d
• 1 p u e r t
• In the prior example,
• p (e0.1 0.8) / (1.25-.8) 0.678
• c (0.678 25 .3220 ) e-0.1 15.34

u - d
u - d
58
Delta

• Delta (D) is the ratio of the change in the price
  of an option to the change in the price of the
  underlying stock
• Generally,
• D cu - cd
• Su - Sd
• In the previous example, D 25 / (125-80) 0.56
• Hedging interpretation
• Delta is the number of shares of stock needed to
  combine with one option to create a riskless
  portfolio