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**Prepared by Paul A. Spindt**

Options Prepared by Paul A. Spindt

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**A Call Option Gives its owner the right (not obligation)**

to buy an asset (the underlying) at a specified price (the exercise price) on (and perhaps before) a given date (the expiration date)

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**A Put Option Gives its owner the right (not obligation)**

to sell an asset (the underlying) at a specified price (the exercise price) on (and perhaps before) a given date (the expiration date)

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**Options Lingo option premium intrinsic value; time value**

European; American long; short covered; naked

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**Wednesday’s closing stock price**

Example Here’s a quote from Wednesday’s Wall Street Journal: -Call Put- SunMic 583/ Jan / /8 Wednesday’s closing stock price Premium Expiration date Option strike price Volume

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Option Payoff: Calls Payoff Stock Price (at Expiration) Strike Price

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Option Payoff: Puts Payoff Stock Price (at Expiration) Strike Price

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**Option Value Intrinsic value Time value**

The intrinsic value of a call is max(0,S-X) The intrinsic value of a put is max(X-S,0) Time value Time value is the option premium minus intrinsic value

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**When S is greater than X, the intrinsic value of the call is $(S-X)**

The Value of a Call Value } When S is greater than X, the intrinsic value of the call is $(S-X) (S-X) S X This call option has an intrinsic value of $3.75 and time value of $3.50 -Call Put- SunMic 583/ Jan /

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**When S is less than X, the intrinsic value of the call is $0**

The Value of a Call Value When S is less than X, the intrinsic value of the call is $0 X This call option has an intrinsic value of $0 and time value of $3.625 -Call Put- SunMic 583/ Jan / /8

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**When S is less than X, the intrinsic value of the put is $(X-S)**

The Value of a Put Value X This put option has an intrinsic value of $1.25 and time value of $2.625. When S is less than X, the intrinsic value of the put is $(X-S) -Call Put- SunMic 583/ Jan / /8

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**When S is greater than X, the intrinsic value of the put is $0**

The Value of a Put Value X This put option has an intrinsic value of $0 and a time value of $2.00 When S is greater than X, the intrinsic value of the put is $0 -Call Put- SunMic 583/ Jan /

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Put-Call Parity In an efficient market two investments with the same payoff ought to have the same price.

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**Put-Call Parity This principle implies that**

the current stock price plus the price of a put

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**Put-Call Parity should equal**

the price of a call plus the PV of the exercise price

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**Stock Price at Expiration**

The Payoff on a Stock Payoff Terminal value of investment in stock A stock is currently selling at $45. A call and a put each with a strike price of $50 and an expiration date 6 months from now are available. Stock Price at Expiration $50 $50

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**Stock Price at Expiration**

The Payoff on a Put Payoff Terminal value of investment in stock (minus $50) Terminal value of investment in put Stock Price at Expiration $0 $50

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**The Payoff on a Stock and a Put**

Terminal value of investment in both stock and put Stock Price at Expiration $50 $50

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**Stock Price at Expiration**

The Payoff on a Call Payoff Terminal value of investment in call Stock Price at Expiration $0 $50

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**Stock Price at Expiration**

The Payoff on a Bond Payoff Terminal value of investment in call (plus $50) Stock Price at Expiration $50 $50 Terminal value of investment in bond

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**The Payoff on a Call and a Bond**

Terminal value of investment in call and bond Stock Price at Expiration $50 $50 Terminal value of investment in bond

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For Example: Here’s a put and a call on SunMic. Each has a strike price of $60. The current stock price is $58.75, so the call is out of the money and the put is in the money. Both expire in one month. -Call Put- SunMic 583/ Jan / /8

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**For Example: Put-call parity implies that -Call- -Put- SunMic**

583/ Jan / /8

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**Determinants of Option Value**

The price of the underlying asset The value of a call rises (the value of a put falls) as the price of the underlying asset rises, all other things equal. The amount an option’s premium changes when the price of the underlying asset changes is called the option’s delta.

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**Determinants of Option Value**

The strike price The value of a call falls (the value of a put rises) as the strike price rises, all other things equal.

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**Determinants of Option Value**

Time to expiration The value of both puts and calls rises as the time to expiration increases, all other things equal. The amount an option’s premium changes when its time to maturity changes is called the option’s theta.

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**Determinants of Option Value**

Volatility The volatility of the underlying asset is a measure of how uncertain we are about future changes in an asset’s value. The more volatility increases, other things equal, the greater the chance that an option will do very well. The value of both puts and calls rises as the volatility of the underlying asset increases.

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**Determinants of Option Value**

The risk-free rate of interest The value of a call rises (the value of a put falls) when the risk-free interest rate rises.

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**The Black-Scholes Formula**

The Black-Scholes pricing formula for a “plain vanilla” call option when the stock price is S, the strike price is X, the risk-free rate is r per annum and the time to expiration is t years is: N(*) is the cumulative standard normal distribution evaluated at *, and

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**The Black-Scholes Formula**

d1 and d2 are functions of the stock price, the strike price, the interest rate, time and volatility: compare

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Normal Distribution

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Example TelMex Jul CB 23/8 -5/ ,703

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Assignment Option Price Calculator Ito’s Dilemma (A) Ito’s Dilemma (B)

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