Baruch MFE MTH 9821 Numerical Methods for Finance

Copyright 2016 @ Yuchen Qi, All rights reserved

• Python 2.7 interpreter, if you wish to use Python 3.0 or above, you only have to change all the print commands which are everywhere in this repo.
• Numpy package with version 1.11.0 or above is a must
• Scipy package is used to generate normal cdf

• Basically all the algos needed for MTH 9821
• Linear Algebra
• Black-Scholes pricer
• Trees pricer
• Monte Carlo pricer
• Finite Difference pricer

Numpy.linalg has much efficient implementation for all the algos here, this is only for class exercise

• Forward and backward substitution
• LU decomposition and Cholesky decomposition All with banded variants

Iterative methods to solve linear system

• Gauss-Sidel
• Jacobi
• Successive over relaxation(SOR) All with banded variants

Implementation of a basic option class and a barrier option class (derived from option class)

Price a plain vanilla European option with Black-Scholes formula and calculate Greeks

NMF_Binomial_Tree, NMF_Fast_Binomial_Tree, NMF_Trinomial_Tree, NMF_Fast_Trinomial_Tree

• Contains tree pricing method and Greeks calculation
• Binomial tree has an implied volatility calculating method using secant method
• Use the Fast variant if able. Plain vanilla American and European optoins are supported

NMF_RND is a pseudo random number generator for uniform random variables or normal random variables

Use numpy.random module instead if able

• Read Control_Variates.py to get an idea how this works, it is not well orgnized because of the assignment
• NMF_Monte_Carlo contains a simple pricer for plain vanilla options
• It is not likely to be completed

NMF_Heat_PDE is the solver of heat pde, it requires NMF_linear_solve and NMF_iter_solve to work

• Includes Forward Euler(fast but not accurate), Backward Euler(balance speed and accuracy), and Crank-Nicolson(slow but accurate) methods to solve the heat pde numerically

NMF_Finite_Difference is the option price solver, it requires NMF_Heat_PDE to work

Has variants for barrier options and options paying discrete dividends