Question

Question 2 (Pricing Call Options) Consider a 11-period binomial model with R=1.05R=1.05, S_0 = 50S 0 ​ =50, u=1/d= 1.08u=1/d=1.08. What is the value of a European call option on the stock with strike K=52K=52, assuming that the stock does not pay dividends? Please submit your answer rounded to two decimal places. So for example, if your answer is 5.4895.489 then you should submit an answer of 5.485.48 or 5.495.49.

Answer 1

Answer:

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Answer 2

Answer

The European call option value = 2.0359

Explanation

Consider S_o=100.

S_u=S_o×4=100 ×1.05=105

S_d=S_o×1/4=100×1/1.05=95.238

Up-move probability π-u=(R-d)/(u/d)

                   = (1.02-(1/1.05))/(1.05-(1/1.05))

                   = 0.642

probability of a down-move π_d=1- π_4=0.307

                 t = 0.

             S_4=105

          C_u=(105-102)=3 call value

              S_d=95.238

C_d value = maxi of (95.258-102.0) =0

Call value C_u = (C_u+_d C_d)1/R

                 = (0.693+0.3070)1/1.02

                 = 2.0352

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