FM5002-HW12-5.2.12

K k s d c r t s k r s d c r t s k t ccompute

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Unformatted text preview: Ke rT e d Σ T 2Π 2 2 T Σ . 0062 1. Suppose that , on a certain stock , the an nual drift is 0.02 and the an nual volatility is 0.35. Suppose that the current share price of the stock is $1. Assume that $1 in vested risk free for on e year grows to e 0.015 dollars. a. Using the B − S Option Pricin g Formula, price a 0.25 − year call option on the stock with a strike price of $1. b. Calibrate the uptick and down tick factors, e u an d e d , of a 50 50 CRR model in which each subperiod is 1 6 of a year. c. Usin g a 3 − subperiod 50 − 50 CRR model, price a 0.25 − year call option on the stock with a strike price of $1. a. We are given that Σ ΣΣ T 0.35, r 0.015, K 1, S0 1, T 0.25. Then 0.175, r r T 0.005, K 0.996257, K’ er ln S0 K’ Σ d , so that Σ 2 d 0.108929 an d d 0.0660714. Plugging in to the Black Scholes formula, we have S0 d K’ d 0.0714828 b. We have that 0.02 Μ an d Σ 12 0.5 u . Then we solve 12 0.02 an d Μ 12 0.35 Σ to obtain 12 0.09933. 0.5 d 0.5 u 0.35 0.5 d u 0.10267, d 3 c. C e 0.015 0.25 i0 3 i 0.5 i 0.5 3i eu i d3i 1 0.086701. 7...
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