Suppose that Bigco is currently trading for $100 per share. We know that in one

Question

Suppose that Bigco is currently trading for $100 per share. We know that in one year Bigco stock will sell for either $150 per share (“good day”) or for $75 per share (“bad day”). No other prices are possible, and the stock does not pay any dividends. The riskless interest rate is 5 percent, so a bond worth B1 next year sells for B0 5 B1 /(1 1 r) today. Stocks, bonds, and options can all be bought or sold, long and short, without any transaction costs.

What is the value of a European call option with a strike price of $100 and expiration in one year?

Explanation / Answer

1) Calculation of value of European call option by using risk neutral method :

Let the probability of attaining maximum price be p

    (150 - 100)*p + (75 - 100)* (1 - p) = 100*(e 0.05 -1)

                             50*p -25 +25*p = 100 (1.05127 - 1)

                                      75*p - 25 = 5.127

                                              75*p = 5.127+25

                                                   p = 0.4017

   The value of European call option is = 0.4017 *(150 - 100(strike price))/1.05127

                                                       = $19.105

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