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Lecture 8 (part 2)

# 75 stock sell call x 35 value of portfolio 30 2250 0

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Unformatted text preview: e same payoffs at expiry: Stock price Buy 0.75 Stock Buy Call (X = \$35) \$30 \$22.50 0 \$50 \$37.50 \$15 Range of Payoff \$15 \$15 Option Pricing Option Pricing Create a riskless hedge: Buy 0.75 shares, Sell call Stock price Buy 0.75 Stock Sell Call (X = \$35) Value of Portfolio \$30 \$22.50 0 \$22.50 \$50 \$37.50 (\$15) \$22.50 Valuing the call option: Assume risk-free rate: 8%, PV of portfolio = \$22.50/1.08 = \$20.83 Price of call = Price of stocks – PV of portfolio to break even = 0.75 x \$40 - \$20.83 = \$9.17 Option Pricing Option Pricing ­ Binomial Option Pricing Model 1 Period Model Sample Portfolio • • Long H amt of Stock Short 1 Call Note: H is the amt of stock which will produce a “Hedged Portfolio”, ie. the position of the portfolio that will be hedged against any change in the price of the asset at expiry. H = Hedge Ratio Option Pricing Option Pricing ­ Binomial Option Pricing Model Assumptions: • 2 possible stock prices (\$30 or \$50) at the end of 1 year. • Current stock price...
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