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428_lecture20_realoption_S09

428_lecture20_realoption_S09 - Lecture 20 Valuation With An...

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Lecture 20 Valuation With An Option Perspective Manny Dong September 23, 2009
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Class of 4/9 in Park Center Two sections: Section 1: 11:40am-1:00pm Students last name starting with A-L Section 2: 4:30pm-6:00pm Students last name starting with M-Z Park Center Second Floor, Sage Hall, by the elevator September 23, 2009
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Outline Review Option provides a different perspective to corporate bond and stock: Corporate Bond Stock Option also provides a different perspective on valuation of investment opportunities. Introduction to Black-Scholes Call Options September 23, 2009
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Naked Option Positions Naked call option position - occurs when an investor buys or sells an call option on a stock without already owning the underlying stock Naked put option positions – occurs when a trader buys or sells a put option without owning the underlying stock September 23, 2009
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Net Payoffs of Long and Short Options S > X S < X Buy A Call with Price C S – X - C - C Sell A Call with Price C -(S – X –C ) =C + X - S C Buy A Put with Price P -P X- S - P Sell a Put with Price P P -(X - S - P) = P+ S - X September 23, 2009
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The current market price of a stock is $100. You hold an expiring option. Should you exercise it, if… It is a call option with exercise price $99 and call price $5? What if exercise price is $101? It is a put option with exercise price $99 and put price $5 ? It is a put option with exercise price $101 and put price $5 ? Always exercise “ in-the-money” option at expiration. Never exercise “ out-of–the-money” option at expiration. Option Exercise Strategy at Expiration Date September 23, 2009
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Factors Affecting Prices Variable Call Put Stock Price + - Exercise Price - + Time to maturity + + Stock volatility + - Interest rates - + September 23, 2009
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Suppose you buy: a call option with exercise price $10 a call option with exercise price $30 and sell: a put option with exercise price of $5 a call option with exercise price of $35 Assuming all have the same expiry date, draw a gross payoff diagram Exercise September 23, 2009
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Review: Put-Call Parity Price of put + price of stock = Price of call + price of bond P + S = C + B P + S = C + PV(X) Long put: P = C + PV(X) – S Short put: -P = - C - PV(X) + S Long stock:  S = C + PV(X) – P Short stock: -S = - C - PV(X) + P Long call:  C = S + P - PV(X) Short call: -C = - S – P + PV(X) September 23, 2009
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Put-Call Parity and Arbitrage Assumptions   Stock price = $46; call price (X = $45) $5. Options expire in 3 months. Risk-free rate for 3-month T-bill is 5%. P + S = C + B P + $46 = $5 + ($45/(1.05) .25 ) P = $3.45 What if the 3-month put option with X = $45 actually sells for  $3  rather  than $3.45? The put is underpriced, so you want to buy it.  To offset the risk you must sell a synthetic put:  - P = S - B - C   September 23, 2009
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Put-Call Parity Arbitrage If stock price is Value of Buy put (actual put) Value Of Short bond Value of short call Value of Buy Stock Net value is 35 10 -45 0 35 0 40 5 -45 0 40 0 45 0 -45 0 45 0 50 0 -45 -5 50 0 55 0 -45 -10 55 0
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