  The Black-Scholes model (sometimes known as the Black-Scholes-Merton model)
gives a theoretical estimate for the price of European options. The price
evolution under this model is described by the Black-Scholes formula, one of
the most well-known formulas in mathematical finance. For their discovery,
Merton and Scholes have been awarded the 1997 Nobel prize in Economics. The
standard method of deriving the Black-Scholes European call option pricing
formula involves stochastic differential equations. This approach is out of
reach for most students learning the model for the first time. We provide an
alternate derivation using the Lindeberg-Feller central limit theorem under
suitable assumptions. Our approach is elementary and can be understood by
undergraduates taking a standard undergraduate course in probability.
