Question

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. 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. Check Answers: PP = $3.35, PC = $2.33 Can't figure out how to get the answers given (for verification).

Answer 1

For solving this types of question one need to understand the binomial option pricing model

Current Stock Price = $ 38

Su = 43.32

Sd = 33.82

Suu = 49.38 ; option price = max(0, (41-49.38) = 0

Sud = 38.55 ; Option price of put= max(0, (41- 38.55) = $2.45

Sdd = 30.1 ; option price of put = max (0, (41 - 30.1) = $10.9

we need to find value of u and d

u = 43.32/38 = 1.14

d = 33.82/38 = .89

probablity of up, p = (e^(r*t) - d)/(u-d ) = .54

Probablity of down = 1-.54 = .46

Value of put at Su = e^(-r*t) {p*option price at Suu + (1-p)*option price at Sud}

= e^(-.025*1) (.54*0 + .46*2.45)

= $ 1.1

Value of put at Sd = e^(-r*t) {p*option price at Sud - (1-p)*option price at Sdd}

= e^(-.025*1) (.54*2.45 + .46 * 10.9)

= $6.18

Vlaue of European put option = e^(-.025 *1) * (.54*1.1 + .46*.6.18)

= $ 3.35

Value of european call using put call parity

c = p + s - PV (x)

= 3.35 + 38 - 41*e^(-2*.025)

= $ 2.33