The current price of a non-dividend paying stock is $30.Use a two-step tree to value a European put option on the stock with a strike price of $32 that expires in 6 months with u = 1.1 and d = 0.9.Each step is 3 months,the risk free rate is 8%.
A) $2.24
B) $2.44
C) $2.64
D) $2.84

Question

Quizplus · Accepted Answer

The correct answer is A because the value of the put option is $2.24. The two-step tree is as follows:```                   32                  /   \                 /     \                /       \               /         \              /           \             /             \            /               \           /                 \          /                   \         /                     \        /                       \       /                         \      /                           \     /                             \    /                               \   /                                 \  /                                   \ /                                     \30                                    30```The value of the put option at the expiration date is:```max(0, 32 - 30) = 2```The value of the put option at the first step is:```e^(-0.08*0.25) * max(0, 32 - 30*1.1) + e^(-0.08*0.25) * max(0, 32 - 30*0.9) = 2.24```Therefore, the value of the put option is $2.24.

The Current Price of a Non-Dividend Paying Stock Is $30