Suppose that firm Ds shares are currently selling for $38. After six months it i

Question

Suppose that firm Ds shares are currently selling for $38. After six months it is estimated that the share price will either rise to $43.32 or fall to $33.82. If the share price rises to $43.32 in six months, six months from that date (1 year from today) the price is estimated to be either $49.38 or $38.55. If the share price falls to $33.82 in six months, six months from that date (1 year from today) the price is estimated to be either $38.55 or $30.10

Suppose that a European put option with an exercise price of $41 is written today and will expire in 1 year. If the six month risk free rate is 2.5 percent, use the binomial model to estimate the current value of the put option.

answer is 3.35$. help please. cant figure it out

Explanation / Answer

Note: Assume equal probability of up and down stock movements

Value of put option today = 3.95/e^0.025*2 = 3.75

Stock Movement Stock Price Exercise the option Payoff Probability Weighted value 1 Up and Up 49.38 No be exercised as X < S 0 0.25 0 2 Up and Down 38.55 Exercised as X > S Payoff = 41 - 38.55 = 2.45 0.25 0.6125 3 Down and Up 38.55 Exercised as X > S Payoff = 41 - 38.55 = 2.45 0.25 0.6125 4 Down and Down 30.1 Exercised as X > S Payoff = 41 - 30.10 = 10.90 0.25 2.725 Total Weighted Value 3.95

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