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# On the Numerical Solution of Black-Scholes Equation

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Numerical Solution of Black-Scholes equation. 1 Introduction Black-Scholes model is used to describe behaviour of derivative instruments like call and put option. The model yields a partial differential equation called the Black-scholes equation which can reduced to the form of the famous heat equation…

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## Introduction

An option is a financial instrument that gives an individual the right to buy or sell an asset, at some time in the future. Options are traded on a number of exchanges throughout the world, the first of which was the Chicago Board Options Exchange (CBOE), which started in 1971.The price V(S,t) of the derivative or the option depends on the price of the underlying S and time t. V(S,t) satisfies the Black Scholes partial differential equation. (1) Where r is the interest free interst rate and ? is the volatility of the underlying. The right to buy the underlying in the future for an agreed upon price , called the Exercise price(E) ,with in a date called the expiry date, is called a Call Option.. Similarly the right to sell the underlying for the Exercise price before the expiry date is the Put Opttion.The time to expiry is the expiry time denoted by T. The pay-off equations for the options gives the boundary conditions for the Black-Scholes equation.The variable t can take values between 0 and T while S can take values from 0 to ? . ...

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