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# Introduction

We show one method of solving the Black-Scholes equation for the value of a call option using the Green's function approach to the diffusion equation. This is suitable to the background of many advanced physics, mathematics, and engineering students.

We consider a stock held at a variable market price x, and whose temporal evolution we treat as only determined by a random walk or a Gaussian probability distribution. This equity is hedged by selling call options at a price w(x,t), which allow a call on the stock at the maturity date t* at the strike price c. The conservative stock holder is then protecting themselves against some possible loss in the stock value by selling some possible profits from a large increase in the stock price. (Since I am not an economist, an arbitrager, a market analyst, a market bull, or even a day trader, I disown any responsibility for any errors or misunderstandings caused by this document.)

We refer the reader to the original Black-Scholes paper[1], to the website of the Nobel Prize in Economics explaining the origin and significance of the method and equation[2], and to a Scientific American article[3] which examines the limitations of the assumptions when applied to the real stock situation.

Next: Boundary Condition Up: Solution of the Black Previous: Solution of the Black
Dennis Silverman
1999-05-20