1. Assume that on October 27, the Nokia Corporation’s stock traded at $15.36. At

Question

1. Assume that on October 27, the Nokia Corporation’s stock traded at $15.36. At the time the stock price was quoted, the most actively traded option for this stock was a call option with November maturity and a strike price of $17.50, which had exactly 30 days until expiration. Assume a US Treasury Bill with the same maturity had an annualized return of 1.20%. The variance of the stock price is 10% annually. You can assume that options for Nokia have European type exercise structure. a) Calculate the Black-Scholes price for the call option described above. b) Calculate the price of a put option that has the same strike price and maturity as the call option above. c) If the call option described above trades for $0.1 in the market, what would you expect the market price of the same call option to be if the stock price increases to $16.15?

Explanation / Answer

a) Black Scholes price for Call option

    d1 = [ ln ( 15.36 / 17.5 ) + ( 0.012 + ( 0.1 / 2) ) * (30/360) ] / ( root 10 * root (1/12) ) = -0.125

    d2 = -0.125 - root(10) * root (1/12) = -1.0378

    C = 15.36 * N(-0.125) - 17.5 * e^(-0.012 * 1/12) * N(-1.0378) = 15.36 * 0.45026 - 17.5 * e^(-0.001) * 0.14917

                                                                                          = 4.30812

b) Price of Put option = 17.5 * e^(-0.001)) * N(1.0378) - 15.36 * N(0.125)

                               = 6.4306

c) Folow procedure in step (a) with S = 16.15

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