Question

What is the price of a European put option with the following parameters? s0 = $42 k = $42 r = 10% sigma = 20% T = 0.5 years (required precision 0.01 +/- 0.01) black scholes equation.PNG As a reminder, the cumulative probability function is calculated in Excel as follows: N(d1) = NORM.S.DIST(d1,TRUE) N(d2) = NORM.S.DIST(d2,TRUE) If the above equations don't load for whatever reason, here are the text versions of the equations as a back-up: c = So*N(d1) - K*e^(-rT)*N(d2) p = K*e^(-rT)*N(-d2) - So*N(-d1) d1 = [ln(So/K) + (r + 0.5*(sigma^2))*T] / [sigma * sqrt(T)] d2 = d1 - sigma*sqrt(T) To validate your equations, you may use the following information to ensure you have it coded correctly: s0 = 22 k = 25 r = 0.1 sigma = 0.2 T = 0.75 d1 = -0.2184 d2 = -0.3916 c = 1.03446 p = 2.22805

Answer 1

S=42,k=42,r=0.1,T=0.5,sigma=0.2

G 14 P(St,t) = Ker(T-t) – S+ + C(St,t) = N(-da)Ker(T-t) – N(-d, s, 17 1 .1 18 19 SO 0.424264 (LN(C19/C20)+(C22+C21^2/2)*C23)/(C21*SQRT(C23)) 20 K 0.282843 F19-C21*SQRT(C23) 21 sigma 0.2 1.428313 C20*EXP(-C22*C23)*NORMSDIST(-F20)-C19*NORMSDIST(-F19) 22 0.1 23 T 0.5 24

p=1.4283