Question

please answer question 4

4. Assume the following information for a stock and a call option written on the stock: 

Exercise price = $45 

Current stock price = $30 

a. Use the Black-Scholes formula to determine the value of the call option. 

b. What is the value of the corresponding put option on the same stock with the same exercise price and time to maturity? 

c. Repeat a and b when the time to expiration is 0.5. 

d. Rercat a and b when the exercise price $35. 

Answer 1

DELTA PINO. I Given Excercise brice (X)= $45 levrrent Stock Price C = $30 Time to expiration Ct = 0.25 Rate - free Rate (r= 0.05 22= 0.25 ¿ = 50.25 = 0.5 calculation of valuation of call (o die dog s7 t/rt 2 | xt. I = Log[ 30 10.05 +0.25 +0.25 کدو گO = Logo 66677 + 0.04375 - 0.17607 + 0.0437.5 - 053 (approx)

DELTA PONS da = di-out = -0.531 - 0.5 = -0.78 . 0.25 Ncd ) = N(-015 3) = ? z A ber Standard Normal Distribution table. 0:53 value=0.2019. 0:53 N(-0:53) = 0.50 -0.2014 Similarly for N C do J = N6-078): ? As berstandard Normal Distribution table = 0178 valece zo. 2823 N(-0.79) = 0.50 - 0.2823 - 28 0.2177 value of cau (C) SL.NC - X ENCd)] = [ 30x02981] - 45 2 [0:2177 ] e0.05x0.25

DELTA POISS 0.2177 0'0/25 = 8.943 - 45 [ 0:2 177 / = 8, 943 - 45 [0.2177] 1.0126 9.675 - 8.943 - = -0.732 Hence value of call is zero. be vale aj Put (P) = x [i-1(d,) - [5 (1-w(2, So [–02193) - L3061-0228 =(34.765 - 21.057) 13.708

DELTA PO NO ANC value of law and put at 0.5 time Expiration der Log 209 30 0.05 + 0.35 0.5 - 0. 505 Log[0.6667] tooges 0.3535 ł - 017607 +0.0875 0.3535 = -0.25 Capprot) = -0.25 -0.5.) 0.5 -0.25 -0.3535 -obo (approt ) -

DELTA PINO N(di) = N(-025) = ? Asper Standard Normal distribution table 0.25 valuez 0.0987 N(-0.25 2 050 0:0987 0.4013 -0.25 - Similarly for NCd2) = N(-0.60) = ? I I value of obos ber Standard Normal table is a 0.2257 NC-obo) = 0.50 -0. 2257 2743 06 value of call (() = SE NdJ- 7 [N (22)] = (30x 0.40137 45 [ 0.8743 45 0.2243 12.039 - 45 +0.2743 20025 - 12.039 - 45 x03743 1.0253 12039 - 12.039 Mence value of call is zero.

Date DELTA PO NO. value of put (P)² + (1 - N(2) - [5 (1-N(21) - 45 1-02743 ]- 30 (1-0.4013) 1.0253 L = 3185 - 17.96) a 13.889