FE 621 Homework

Repository to store homework for FE 621 (Computational Methods in Finance) taught by Professor Ionut Florescu at the Steven Institute of Technology in Spring Semester 2019.

Functionality Overview

Black Scholes Model Pricing (Analytical)

• Asian (i.e. average value) Equity Options: https://github.com/rukmal/FE-621-Homework/tree/master/fe621/black_scholes/asian
• Barrier Equity Options: https://github.com/rukmal/FE-621-Homework/tree/master/fe621/black_scholes/barrier
• Vanilla Equity Options: https://github.com/rukmal/FE-621-Homework/tree/master/fe621/black_scholes
• Vanilla Greeks: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/black_scholes/greeks.py
• Vanilla Parity: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/black_scholes/parity.py

Monte Carlo Simulations

Note: All option pricing functions are under the Black Scholes model heuristic.

• General Simulation Driver: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/monte_carlo/monte_carlo.py
• Simple Geometric Brownian Motion Equity Option Pricing: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/monte_carlo/option_pricing/simple_gbm.py
• Delta-Based Control Variates Method Variance-Reduced Equity Option Pricing: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/monte_carlo/option_pricing/control_variates.py
• Antithetic Variates Method Variance-Reduced Equity Option Pricing: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/monte_carlo/option_pricing/antithetic_variates.py
• Antithetic Variates Delta-Based Control Variates Method Variance-Reduced Equity Option Pricing: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/monte_carlo/option_pricing/antithetic_control_variates.py

Numerical Differentiation/Integration

• Numerical Differentiation: https://github.com/rukmal/FE-621-Homework/tree/master/fe621/numerical_differentiation
• Simpson's Quadrature Rule (Numerical Integration): https://github.com/rukmal/FE-621-Homework/blob/master/fe621/numerical_integration/simpsons.py
• Trapezoidal Quadrature Rule (Numerical Integration): https://github.com/rukmal/FE-621-Homework/blob/master/fe621/numerical_integration/trapezoidal.py

Optimization (Numeric; 1D)

• Bisection Method: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/optimization/bisection.py
• Newton's Method: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/optimization/newton.py

Lattice Based (Tree) Pricing Models

Note: All option pricing functions are under the Black Scholes model heuristic.

• General Tree Driver: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/tree_pricing/general_tree.py
• Binomial Trigeorgis Additive Vanilla Option Pricing: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/tree_pricing/binomial/trigeorgis.py
• Binomial Trigeorgis Additive Barrier Option Pricing: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/tree_pricing/binomial/barrier.py
• Trinomial Additive Vanilla Option Pricing: https://github.com/rukmal/FE-621-Homework/blob/master/fe621/tree_pricing/trinomial/trinomial_price.py