Question

QUESTION 2 12 points Save Answer A European call option written on one share of Crook & Crook, Inc. has the following parameter values: S= $33, X = $37, r = 7% p.a., 0 = 25% p.a., T = 8 months. Find the value of d2, rounded to 4 decimals (e.g., 0.0712). NOTE: Use the continuous time version of the equation (i.e., do NOT use the book's version)

Answer 1

The Black-Scholes Model; European call option formula

C = SN (d1) - N (d2) Xe ^ (-rt)

Where

C = call value =?

S = current stock price =$33

N = cumulative standard normal probability distribution

t = days until expiration = 8 months or 8/12 = 0.67 years

Standard deviation, SD = 25% = 0.25

X = option strike price = $37

r = risk free interest rate =7% or 0.07 per year

Formula to calculate d1 and d2 are -

d1 = {ln (S/K) +(r+ σ^2 /2)* t}/σ *√t

= {ln (33/37) + (0.07 + (0.25^2)/2) * 0.67} / 0.25 * √0.67

= -0.2298

d2 = d1 – σ *√t = -0.2298 – 0.25 * √0.67 = -0.4339