Question

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

Answer 1

Answer:

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