Question

Problem1 A stock is currently trading at S $40, during next 6 months stock price will increase to $44 or decrease to $32-6-month risk-free rate is rf-2%. a. [4pts) What positions in stock and T-bills will you put to replicate the pay off of a European call option with K = $38 and maturing in 6 months. b. 1pt What is the value of this European call option? Problem 2 Suppose that stock price will increase 5% and decrease 5% every year. The stock does not pay dividend and curretly is tradding at S-$100. Annual risk-free rate is rf-3%. a. 3pts Construct a two-year binomial tree for the value of the stock b. 3pts Calculate the value of a European call option on the stock with an exercise price of $101 c. 3pts Calculate the value of a European put option on the stock with an exercise price d. [1pt Confirm that your solutions for the values of the call and the put satisfy put-call e. 5pts] Extra credit and not required] Calculate the value of an American put option on of $101 parity the stock with an exercise price of $101 Problem 3 [4pts Suppose a stock with an annual volatility of 20%, is trading at $20 and do not pay dividend. Annual risk-free rate is r,-1%. Use the Black-Scholes formula to find the value of a call and put options with a strike price of K $25 and time to maturity of 6 months

Answer 1

Problem 3

Formula of black scholes

C= St N(D1) - Ke^{​​​​​ -rt} N(D2)

Where

D1 =[ Ln S_{​​​​​​}​​​​​​t/ K + ( r + Variance / 2) t ] / ( SD√t)

D2 = D1- SD √t

Where

C = Price of call option

S = Current stock prive

K = strike price

r = risk free rate

t = time to maturity

N = normal distribution

Hence

C = $20 N(D1) - $25 e ^-.01*(6/12) N (D2)

D1 = [Log ($20/$25) + (0.01+ 0.20 ² / 2) (6/12)] / (0.20 √6/12)

D2 = D1 - (0.20 *√6/12)

e is the exponential value measuring 1.0272