Question

QUESTION 3 15 points Save Answer A European call option written on one share of Medident Corp. has the following parameter values: S = $220, X = $200, r = 5% p.a., sigma = 20% p.a., T 9 months. Find the call option's premium, rounded to 2 decimals (e.g., 3.24). Do NOT include the S sign in your answer; write only the numerical value. NOTE: Use the continuous time version of the Black-Scholes equation (i.e., do NOT use the book's version).

Answer 1

t=9/12 =0.75
d1=[ln(S/X) + (R – d + σ^2 / 2) × t] / (σ ×t^0.5) =(Ln(220/200)+(5%-0%+20%^2/2)*0.75)/(20%*0.75^0.5) =0.853382

N(d1) using NORMSDIST function of excel =NORMSDIST(0.853382) =0.803276

d2 =d1-σ*t^0.5 =0.853382-20%*0.75^0.5=0.680177
N(d2) using NORMSDIST function of excel =NORMSDIST(0.680177) =0.751804

Call Option =C = S * N(d1) – X × e–Rt × N(d2) =220*0.803276-200*EXP(-5%*0.75)*0.751804 =31.89