FM5002-HW12-5.2.12

01 dollars assume that the curren t price is 3 per

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Unformatted text preview: ’ 2.99754, r e 1.00082 ln S0 K’ Σ 0.00234834 0.0430037, so that d Σ 2 d 0.045352 an d d 0.0406554. Plugging in to the Black Scholes formula, we have S0 d K’ d 3 0.2078387 2.99754 0.1941551 0.0276856. 0061 2. Let C r , Σ , T, S, K den ote the Black Scholes price on a T year European call option, struck at K, with current un derlying price S, assumin g the ann ual force of in terest is r , an d the an n ual volatility Σ . a. Compute r , Σ , T, S, K b. Compute r , Σ , T, S, K S C S d S d S d S e d 2 T S C T S T d Ke r T e d 2 2 1 rT d e Σ T TS 2 e rT Ke Σ 2 1 2Π d 2 2 2Π 1 Σ TS d. TS Σ d d d T r Σ S d 2Π Ke K’ 2 e TS d 2Π S d rT 2 d 1 T Ke d Σ d d d 2 2Π b. K’ K’ S d C r , Σ , T, S, K . r S d C r , Σ , T, S, K . T c.Compute Ρ r , Σ , T, S, K a. C r , Σ , T, S, K . S T 4 rT S T e d 2 2 r 2Π ln S0 e r Σ T Ke T 2Σ T K Σ ln S0 e r T 4 Tr d 2 Kr T T . T 2Σ Σ T K FM5002−HW12−5.2.12.nb c. r CS d Ke r d d rT r d S e d 2 2 2Π T Σ...
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This note was uploaded on 01/19/2014 for the course MATH 5002 taught by Professor Adams during the Spring '08 term at Minnesota.

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