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A stock price is currently Ksh40. Over each of the next two 3-month periods it is...

A stock price is currently Ksh40. Over each of the next two 3-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 12% per annum with continuous compounding. Suppose that the volatility σ is 9.53% and ∇ is 0.25.

  1. What is the value of a 6-month European put option with a strike price of Ksh42?                                                                                                                    

ii. What is the value of a 6-month American call option with a strike price of Ksh42

Solutions

Expert Solution

ans.

            TREE TO EVALUATE FOR AMERICAN AND EUROPEAN PUT OPTION

(A)

now risk neutral probability for up move is ,

                p = [e^(0.12*3/12) - 0.90]/(1.1-0.9)

                p = 0.652

hence value of european option is = [0.652*0.347*2*2.4 + 0.347^(2)*9.6]e^(-0.12*6/12)

                              so,answer is = 2.118

(B)

here value of americam put option is 2.537 beacuse as shown on the tree the american put option is third number at each node.

                          so, answer is = 2.537

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