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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 method
  • Explicit method
  • Implicit method
I thank you very much in advance and I wish to have your valuable support.

POSTED BY: Anais Hulot
4 Replies
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 BY: Sander Huisman
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:
T=3 years

So could anyone please help.


POSTED BY: Anais Hulot
The first step would be to write out these numerical methods for a simple stochastic differential equation.

I would reccomend this 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 BY: Sean Clarke
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.
POSTED BY: Moderation Team
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