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CHAPTER 20 Options Markets: Introduction

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Buy - Long Sell - Short Call Put Key Elements – Exercise or Strike Price – Premium or Price – Maturity or Expiration Option Terminology

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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 Market and Exercise Price Relationships

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Figure 20.1 Stock Options on IBM

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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 American vs. European Options

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Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options Different Types of Options

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Notation Stock Price = S T Exercise Price = X Payoff to Call Holder (S T - X) if S T >X 0if S T < X Profit to Call Holder Payoff - Purchase Price Payoffs and Profits at Expiration - Calls

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Payoff to Call Writer - (S T - X) if S T >X 0if S T < X Profit to Call Writer Payoff + Premium Payoffs and Profits at Expiration - Calls

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Figure 20.2 Payoff and Profit to Call Option at Expiration

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Figure 20.3 Payoff and Profit to Call Writers at Expiration

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Payoffs to Put Holder 0if S T > X (X - S T ) if S T < X Profit to Put Holder Payoff - Premium Payoffs and Profits at Expiration - Puts

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Payoffs to Put Writer 0if S T > X -(X - S T )if S T < X Profits to Put Writer Payoff + Premium Payoffs and Profits at Expiration – Puts Continued

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Figure 20.4 Payoff and Profit to Put Option at Expiration

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InvestmentStrategyInvestment Equity onlyBuy stock @ 100100 shares$10,000 Options onlyBuy calls @ 101000 options$10,000 Calls plus billsBuy calls @ 10100 options $1,000 Buy T-bills @ 3% $9,000 Yield Equity, Options, & Bills

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IBM Stock Price $95$105$115 All Stock$9,500$10,500$11,500 All Options$0 $5,000$15,000 Calls plus bills $9,270 $9,770$10,770 Payoffs

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IBM Stock Price $95$105$115 All Stock-5.0%5.0% 15% All Options-100% -50% 50% Calls plus bills -7.3%-2.3% 7.7% Rates of Return

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Figure 20.5 Rate of Return to Three Strategies

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Table 20.1 Value of Protective Put Portfolio at Option Expiration

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Figure 20.6 Value of a Protective Put Position at Option Expiration

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Figure 20.7 Protective Put versus Stock Investment (at-the-money option)

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Table 20.2 Value of a Covered Call Position at Expiration

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Figure 20.8 Value of a Covered Call Position at Expiration

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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 Option Strategies

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Table 20.3 Value of a Straddle Position at Option Expiration

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Figure 20.9 Value of a Straddle at Expiration

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Table 20.4 Value of a Bullish Spread Position at Expiration

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Figure 20.10 Value of a Bullish Spread Position at Expiration

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Buy one call and write one put Payoff S T X Call owned0S T – X Put written-(X – S T ) 0 Total payoff S T – X S T – X Since the payoff on (call + put) options is equal to leveraged equity, their prices must be equal: C – P = S 0 – X/(1 + r f ) T Put Call Parity Derivation

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If the prices are not equal arbitrage will be possible or C – P = S 0 – X/(1 + r f ) T Put Call Parity

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Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 5% Maturity = 1 yr X = 105 C – P = S 0 – X/(1 + r f ) T 17 – 5 > 110 – 105/(1 + 0.05) Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative Put Call Parity - Disequilibrium Example

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Table 20.5 Arbitrage Strategy

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Optionlike Securities Callable Bonds Convertible Securities Warrants Collateralized Loans

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Figure 20.11 Values of Callable Bonds Compared with Straight Bonds

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Figure 20.12 Value of a Convertible Bond as a Function of Stock Price

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Exotic Options Asian Options C = Max[mean S – X, 0] Look-back Options C = Max [S max – X, 0] Digital Options C = $100 if S T > X 0 if S T < X

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Barrier Options Down-and-Out Barrier Options C = Max[S T – X, 0] if S t > B 0 if S t < B Down-and-In Barrier Options C = Max[S T – X, 0] if S t < B 0 if S t > B

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