Question

1. If d1=.15, What is N(d1)? (round to 4 decimal places)

2. S₀=105; X=100; r=.02; T=60 days; standard deviation of daily returns = .012; Assume 365 calendar days in a year and 255 trading days in a year. Assume N(d1) =0.76 and N(d2) = 0.74 (irrespective of your calculations for d1 and d2), what is the price of a call option according to Black-Scholes? (round to 2 decimal places)

Answer 1

Price of call option = [ S * N( d1 ) ] - [ X * e^-rt * N ( d2 ) ]

S - Spot Rate

X - Strike Price

e^-rt - PVF discounted continously

e-rt :
= e^-0.02*0.1644
= e^-0.0033
= 0.9967

Value of Call = [ S * N( d1 ) ] - [ X * e^-rt * N ( d2 ) ]
= [ $ 105 * 0.76 ] - [ $ 100 * 0.9967 * 0.74 ]
= [ $ 79.8 ] - [ $ 73.7558 ]
= $ 6.04

Price of call option is $ 6.04