The current price of a non-dividend-paying stock is $40. Over the next year it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. What is the value of each option using a one-period binomial model? The risk-free interest rate is 2% per annum. Assume non continuous compounding. Show work, step by step. A. $3.93B. $2.93C. $1.93D. $0.93

D. $0.93

Explanation:

Upmove (U) = High price/current price

= 42/40

= 1.05

Down move (D) = Low price/current price

= 37/40

= 0.925

Risk neutral probability for up move

q = (e^ (risk free rate*time) - D) / (U-D)

= (e^ (0.02*1) - 0.925) / (1.05-0.925)

= 0.76161

Put option payoff at high price (payoff H)

= Max (Strike price-High price, 0)

= Max (41-42,0)

= Max (-1,0)

= 0

Put option payoff at low price (Payoff L)

= Max (Strike price-low price, 0)

= Max (41-37,0)

= Max (4,0)

= 4

Price of Put option = e^ (-r*t) * (q*Payoff H + (1-q) * Payoff L)

= e^ (-0.02*1) * (0.761611*0 + (1-0.761611) * 4)

= 0.93

Therefore, The value of each option using a one-period binomial model is 0.93