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. Each step is 3 months, the risk free rate is 8%, and u = 1.1 and d = 0.9.
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:```             S0 = $30            /     \           u       d          $33     $27         /   \    /   \        u     d  u     d       $36.3     $29.7 $30     $24.3```The value of the put option at the expiration date is:```V(T) = max(0, K - S(T))```where:* V(T) is the value of the put option at the expiration date* K is the strike price* S(T) is the stock price at the expiration dateIn this case, the strike price is $32 and the stock price at the expiration date can be either $36.3, $29.7, $30, or $24.3. Therefore, the value of the put option at the expiration date is:```V(T) = max(0, 32 - 36.3) = 0V(T) = max(0, 32 - 29.7) = 2.3V(T) = max(0, 32 - 30) = 2V(T) = max(0, 32 - 24.3) = 7.7```The value of the put option at time t = 0 is:```V(0) = e^(-r*t) * [p*V(u) + (1-p)*V(d)]```where:* V(0) is the value of the put option at time t = 0* r is the risk-free rate* t is the time to expiration* p is the probability of an up move* V(u) is the value of the put option at time t = 1 and stock price = S(u)* V(d) is the value of the put option at time t = 1 and stock price = S(d)In this case, the risk-free rate is 8%, the time to expiration is 6 months, the probability of an up move is 50%, and the values of the put option at time t = 1 are:```V(u) = 0V(d) = 2.3```Therefore, the value of the put option at time t = 0 is:```V(0) = e^(-0.08*0.5) * [0.5*0 + 0.5*2.3] = $2.24```

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