A derivation of the Black-Scholes option pricing model using a central\n limit theorem argument

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