# Numerical Analysis of Non-linear Black Scholes using finite differences

Posted 10 years ago
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 Could anyone plz help me writing the mathematica codes for the Numerical analysis of Non-linear Black Scholes equations using the following finite difference methods:Crank-Nicolson methodExplicit methodImplicit methodI thank you very much in advance and I wish to have your valuable support.anais.
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Posted 10 years ago
 Hi Anais, you can use ReplaceAll to substitute values in equations. or define values for S E r D T t before inputting the equations. These should be differential equations right? i don't see any derivatives in your equations? Without those you can not setup the finite differences.
Posted 10 years ago
 Hi friends,I think that i've been able to write the code for solving the option price for Black Schole equation.d1 = (log[S/E] + (r - D + 0.5 \^2)*(T - t))/(\*\{T - t})d2 = (log[S/E] + (r - D - 0.5 \^2)*(T - t))/(\*\{T -t})S*\[Epsilon][-D*(T - t)]*N (d1) - E*\[Epsilon][-r*(T - t)]*N (d2)But unfortunately, I don't know how to enter the followinf data to obtain the option price:S=$50E=$50r=5%sigma=25%T=3 yearsSo could anyone please help.Thanks.Regards,anais
Posted 10 years ago
 The first step would be to write out these numerical methods for a simple stochastic differential equation.I would reccomend this pdf: http://www.caam.rice.edu/~cox/stoch/dhigham.pdf, which is what I first used when looking into this area.This covers forward and backward euler for a simple example equation in matlab, but the code is very simple. The corresponding code in Mathematica would be very similar.
Posted 10 years ago
 This does not seem like a small project. You should start implementing this yourself and when encounter a problem come back and ask a more specific question. A good place to start are these numerous Demonstrations on Black Scholes.