Question

a. Price a call option using the two-period binomial model assuming the following data.

S=120,X=80,u=0.2, d=-.2,and r=0.10 per period

b. What is the hedge ratio for this call option?

c. If the call option were priced at $55, what would an arbitrageur do? Discuss an exact strategy?

Answer 1

S = 120, X = 80, u = 1.2, d = 0.8 and r = 0.1

Since time is not given assumed t = 1 yr

P = (e^rt - d)/(u-d)

P = (e^0.1*1 - 0.8)/(1.2-0.8) = (1.1052 - 0.8)/ (0.4) = 0.3052/0.4 = 0.763

1-P = 1-0.763 = 0.237

The figures in the () shows the value.

At node B price = e^-0.1*1 [ 0.763*92.8 + 0.237*35.2] = 0.9049 [70.8064+8.3424] = 71.6218

At node C price = e^-0.1*1 [0.763*35.2 + 0.237*0] = 0.9049 [26.8576 + 0] = 24.3034

At node A price = e^-0.1*1 [71.6218*0.763 + 24.3034*0.237] = 0.9049 [ 54.6474 + 5.76] = 54.6627

Price of call option = $54.6627

Hedge ratio = -1

If call option was priced at $55 then the arbitrageur would sell the call option as the value of call is $54.6627 whereas the market price is $55.