Question

A stock is currently selling for $50. The stock price could go up by 10 percent or fall by 5 percent each month. The monthly risk-free interest rate is 1 percent. Calculate the price of an American put option on the stock with an exercise price of $55 and a maturity of two months. (Use the two-stage binomial method.)

a. $5.10
b. $3.96
c. $4.78
d. $1.19

Answer 1

$5.10

Step-by-step explanation:

where interest rate = monthly rate*10 = 1*12 = 12%

Time period t in years = 1/no. of months in a year = 1/12 = 0.8333

50 = [55(x) + 47.5(1-x)]/(1.01) ; x = 0.4; 1-x = 0.6Payoffs at the end of month-2: $10.5; $2.25 ; and zero; [Exercise price = $50]End of one month values: [(10.5)(0.4) + 2.25(0.6)]/1.01 = 5.495 and [2.25(0.4) + 0]/1.01 = 0.891Price of the call option = [5.495(0.4) + (0.891)(0.6)]/1.01 = 2.71