Please help me solve and workout this problem, all parts, very urgent! Thank you
ID: 2768210 • Letter: P
Question
Please help me solve and workout this problem, all parts, very urgent! Thank you, I give thumbs up!!
1. 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.
a. Sketch the tree diagram of price changes over the year.
b. 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.
c. Use Put-Call parity to find the value of a call option written on the same shares with the same exercise price and expiration date.
Explanation / Answer
Ans;
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