L16_3710 - Ch16. Option Valuation What determines option...

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•1 Investment Analysis: Prof. Peng 1 Ch16. Option Valuation What determines option prices? How is option priced? How to replicate and hedge options? How to arbitrage? Investment Analysis: Prof. Peng 2 Time Value and Intrinsic Value
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•2 Investment Analysis: Prof. Peng 3 Determinants of option values Factors affecting call option value Stock Price: call (+)/put (-) Exercise price: call (-)/put (+) Volatility: call (+)/put (+) Time to expiration: call (+)/put(?) Risk free rate: call (+)/put (-) Dividend payout: call (-)/put (+) Some notations: C: call option value; P: put option value; Investment Analysis: Prof. Peng 4 Continuous compounding Present value of $1 T years from now: Discreet period compounding with EAR: Continuous compounding with annualized continuously compounded rate when the compounding interval approaches zero: T r PV ) 1 ( 1 rT e PV
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•3 Investment Analysis: Prof. Peng 5 Black-Scholes Model The call option price is equal to N ( d ) is a cumulative normal function measures the probability (risk adjusted) that option will mature in the money Xe -rT N ( d 2 ) present value of expected payable S 0 N ( d 1 ) present value of expected receivable Hedge Ratio for Call ( delta ) ) ( ) ( 2 1 0 0 d N Xe d N S C rT   T d d T T r d X S 1 2 2 1 , ) ( ln 2 0 ) ( 1 d N S C H Investment Analysis: Prof. Peng 6 Black-Scholes Model Q : if S = 100, X = 95, T = 0.25, r = 0.1, σ = 0.5 What is the call option price? How should we hedge the call position? A : The portfolio with 1 call and -0.67 shares 70 . 13 94 . 52 64 . 66 5714 . 0 95 6664 . 0 100 5714 . 0 ) 18 . 0 ( ) ( 6664 . 0 ) 43 . 0 ( ) ( 18 . 0 25 . 0 5 . 0 43 . 0 , 43 . 0 25 . 0 5 . 0 25 . 0 ) 2 5 . 0 1 . 0 ( ) 95 / 100 ln( 25 . 0 1 . 0
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L16_3710 - Ch16. Option Valuation What determines option...

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