Derive the Black-Scholes formula to represent the relationship between the price of an option and the price of its underlying stock
Let C be the value of a call option, with
S = current price of the underlying stock
K = the strike price
ln = natural logarithm [to base e]
r = interest rate
T = time to expiration
? = standard deviation of returns on underlying stock
N1(d1) and N2(d2) = cumulative standard normal distribution functions.
Then,
C = SN(d1) - Ke-rTN(d2),
With
d1 = ln(S/K) + [(R + ?2?2??? ? ??T and d2 = d1 - ??T
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