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

Question

Suppose that firm Ds shares are currently jelling for $38. After six months it it estimated that the share price will either rise to $43.32 or fall to $3382. If the share price ns>> to $43 J2 in months, ox months from that date (I year from today) the price is estimated to be other $49.18 or $38.55. If the share price falls to $3382 in six months, six months from that dale (I year from today) the price is estimated to be either $3835 or $30.10. a. Sketch the tree diagram of price changes ova the year. b. suppose that a European put option with an exercise price of $41 is written today and will expire in I year. If tic 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 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

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