1. Lecture 7 – Finite difference scheme for option pricing
It is a method based on the numerical resolution of the partial differential equation (PDE) of Black & Scholes.
It is based on the discretization of:
time;
underlying stock price
option price
PDE of Black & Scholes
It is equivalent from a mathematical point of view to a trinomial tree
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2. Finite difference – explicit method
Fix the borderline condition (i.e. the final condition for t = option expiry).
The equations are solved according to a backward recursive scheme starting from maturity time, getting Fi,j in term of Fi+1,j.
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3. Finite difference - convergence
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4. Finite difference – pros and cons
Simple to be implemented
It is possible to use acceleration methods
American options can be managed
Limited to low dimensional problems
Ad hoc implementations are required basing on contract typology.
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