金融工程课件 (20)

20-20
Put-Call Parity Relationship
ST < X
Payoff for Call Owned Payoff for Put Written -( X -ST) Total Payoff ST - X 0 0
ST > X
ST - X
ST - X
20-21
Payoff of Long Call & Short Put
20-3
Market and Exercise Price Relationships
In the Money - exercise of the option would be profitable. Call: market price>exercise price Put: exercise price>market price Out of the Money - exercise of the option would not be profitable. Call: market price>exercise price Put: exercise price>market price At the Money - exercise price and asset price are equal.
Investment $10,000
1000 options $10,000 $1,000 $9,000
Buy calls @ 10 100 options Buy T-bills @ 2% Yield
20-13
Equity, Options & Leveraged Equity - Payoffs
IBM Stock Price
$95
All Stock -5.0%
$105
5.0%
$115
15%
All Options
Lev Equity
百度文库
-100%
-7.3%
-50%
-2.3%
50%
7.7%
20-15
Protective Put
Use - limit loss Position - long the stock and long the put
Stock Price
20-12
Equity, Options & Leveraged Equity - Text Example
Investment Equity only Options only Leveraged equity
Strategy Buy stock @ 100 300 shares Buy calls @ 10
20-23
Put Call Parity Disequilibrium Example
Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 10.25% Maturity = .5 yr X = 105 C - P > S0 - X / (1 + rf)T 17- 5 > 110 - (105/1.05) 12 > 10 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative.
Payoff
Stock
ST < X
ST
ST > X
ST
Put
X - ST
0
20-16
Protective Put Profit
Profit
Stock Protective Put Portfolio
-P
ST
20-17
Covered Call
Use - Some downside protection at the expense of giving up gain potential.
20-5
Different Types of Options
Stock Options
Index Options Futures Options Foreign Currency Options Interest Rate Options
20-6
Payoffs and Profits on Options at Expiration - Calls
Payoff
Combined = Leveraged Equity Long Call
Stock Price Short Put
20-22
Arbitrage & Put Call Parity
Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal. C - P = S0 - X / (1 + rf)T If the prices are not equal arbitrage will be possible.
20-1
Options Markets: Introduction
20-2
Option Terminology
Buy - Long Sell - Short Call Put Key Elements
- Exercise or Strike Price - Premium or Price - Maturity or Expiration
20-9
Payoffs and Profits at Expiration - Puts
Payoffs to Put Holder 0 if ST > X (X - ST) if ST < X Profit to Put Holder Payoff - Premium
20-10
Payoffs and Profits at Expiration - Puts
20-4
American vs European Options
American - the option can be exercised at any time before expiration or maturity.
European - the option can only be exercised on the expiration or maturity date.
20-24
Put-Call Parity Arbitrage
Position Buy Stock Borrow X/(1+r)T = 100 Sell Call Buy Put Total
Immediate Cashflow -110 +100 +17 -5 2
Cashflow in Six Months ST<105 ST> 105 ST -105 0 105-ST 0 ST -105 -(ST-105) 0 0
20-19
Option Strategies
Straddle (Same Exercise Price) Long Call and Long Put Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration. Vertical or money spread: Same maturity Different exercise price Horizontal or time spread: Different maturity dates
Position - Own the stock and write a call.
Payoff Stock Call ST < X ST 0 ST > X ST - ( ST - X)
20-18
Covered Call Profit
Profit
Stock
Covered Call Portfolio -P ST
IBM Stock Price
$95
All Stock $9,500
$105
$10,500
$115
$11,500
All Options
Lev Equity
$0
$9,270
$5,000
$9,770
$15,000
$10,770
20-14
Equity, Options & Leveraged Equity - Rates of Return
Payoffs to Put Writer 0 if ST > X -(X - ST) if ST < X Profits to Put Writer Payoff + Premium
20-11
Profit Profiles for Puts
Profits
Put Writer
0
Put Holder
Notation Stock Price = ST Exercise Price = X Payoff to Call Holder (ST - X) if ST >X 0 if ST < X
Profit to Call Holder Payoff - Purchase Price
20-7
Payoffs and Profits on Options at Expiration - Calls
20-25
Optionlike Securities
Callable Bonds Convertible Securities Warrants Collateralized Loans
20-26
Exotic Options
Asian Options Barrier Options
Lookback Options
Currency Translated Options
Binary Options
Payoff to Call Writer
- (ST - X) if ST >X
0
if ST < X
Profit to Call Writer
Payoff + Premium
20-8
Profit Profiles for Calls
Call Holder
Profit
0
Call Writer
Stock Price