FM5002-HW12-5.2.12

# 5 that the an n ualized volatility is 40 use the 70 30

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Unformatted text preview: the stock at the en d of the 100 days. a. We compute that 0.025 Μ 0.0000171233, an d 4 365 0.35 0.0104685, so that Σ 4 365 0.7 u 0.3 d Μ 0.000034246575, and 0.7 0.3 u d Σ 0.0091599186. Solving, we con clude that u 0.00603082 an d d −0.0139578. b. Using u and d as above, we have the expression for the expected price of the stock 400 5 i0 400 i 0.7 i 0.3 400 i eu i d 400 i dollars. 0061− . Price a 30 − day European call option on a stock, usin g the Black − Scholes Option Pricin g Formula. 1 Assume that the ann ual drift is 2 . Assume that the ann ual volatility is 35 . Assume that the an nual force of in terest is 1 . That is, \$1, in vested risk free, grows, after one year, to e 0.01 dollars. Assume that the curren t price is \$3 per share, an d that the strike price is also \$3 per share. 6 FM5002−HW12−5.2.12.nb We are given that Σ T 30 0.01, K 3, an d S0 3. Then 0.0821918, 365 T ΣΣ 0.35, r 0.0860073, r r T 0.000821918, K 3 K...
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