Find the values of the 5 -month call option of Example 19.1 using the same trinomial lattice used in that example but employing the utility function \(U(x)=\sqrt{x}\). What is \(\alpha\) ?

Transcribed Image Text:

Example 19.1 (A 5-month call) As a specific example let us consider the 5-month call option studied The underlying stock had S(0) = $62, = .12, and o = .20. The risk-free rate is r = 10% per annum, and the strike price of the option is K = $60. For better accuracy we use a trinomial lattice with 1-month periods. To match the parameters of the stock, we decide on the trinomial parameters u = 1.1, d=1/u, and the middle branch has a multiplicative factor of 1. To find the real probabilities we must solve the equations that correspond to: (1) having the probabilities sum to 1, (2) matching the mean, and (3) matching the variance. These equations, first given in Section 15.7, are P+P2+ P3=1 upi+p2+dp3 = 1+At upi+p2+dp3=0 At+ (1+At). They have solution p = .228, p2 = .632, and p3=.140.