Black-Scholes Option Pricing Formula

In their 1973 paper, The Pricing of Options and Corporate Liabilities, Fischer Black and Myron Scholes published an option valuation formula that today is known as the Black-Scholes model. It has become the standard method of pricing options.

The Black-Scholes formula calculates the price of a call option to be:

C = S N(d₁) - X e^-rT N(d₂)

where

	C = price of the call option
	S = price of the underlying stock
	X = option exercise price
	r = risk-free interest rate
	T = current time until expiration
	N() = area under the normal curve
	d1 = [ ln(S/X) + (r + σ2/2) T ] / σ T1/2
	d2 = d1 - σ T1/2

Put-call parity requires that:

P = C - S + Xe^-rT

Then the price of a put option is:

P = Xe^-rT N(-d₂) - S N(-d₁)

Here is an online calculator: http://www.blobek.com/black-scholes.html