Advanced Computational Methods in Financial Engineering

Repository Overview

This repository contains implementations of advanced computational methods for pricing and analyzing complex financial derivatives and securities. The work encompasses Monte Carlo simulation, finite difference methods, tree-based algorithms, and various numerical techniques applied to options, fixed income securities, and structured products.

Course: MGMTMFE 432 - Computational Methods in Finance
Institution: UCLA Anderson School of Management
Author: Vikalp Thukral

Projects

Project 1: Foundational Option Pricing Methods

Implementation of core computational techniques for derivative pricing:

• Binomial and Trinomial Trees: American and European options with discrete dividends
• Monte Carlo Simulation: Asian options, variance reduction techniques
• Implied Volatility: Newton-Raphson and bisection methods
• Finite Difference Methods: Explicit, implicit, and Crank-Nicolson schemes for American puts

Key Methods: Tree models, Monte Carlo with control variates and antithetic variables, PDE solvers

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Project 2: Advanced Options and Term Structure Models

Extension to complex derivatives and interest rate products:

• Exotic Options: Lookback options, barrier options with rebates
• Interest Rate Models: Vasicek and CIR short rate models
• Monte Carlo Applications: Path-dependent options, interest rate derivatives
• Numerical Integration: Quadrature methods for option pricing

Key Methods: Advanced Monte Carlo, analytical solutions, Richardson extrapolation, term structure modeling

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Project 3: Exotic Derivatives and Fixed Income Securities

Advanced implementations of multi-factor models and structured products:

• Jump-Diffusion Models: Default option valuation with Poisson jumps
• Stochastic Volatility: Down-and-Out puts under Heston-type dynamics
• Fixed Income: CIR and G2++ models for bonds and options
• Mortgage-Backed Securities: MBS pricing with prepayment modeling, IO/PO tranches, OAS computation

Key Methods: Two-factor models, full truncation schemes, Numerix prepayment model, implicit FDM

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Technical Stack

• Language: Python 3.x
• Core Libraries: NumPy, SciPy, Pandas
• Visualization: Matplotlib, Seaborn
• Numerical Methods: Monte Carlo, finite differences, tree algorithms, root-finding, quadrature

Repository Structure

Advanced-Computational-Methods/
├── Project1/
│   ├── README.md
│   ├── implementation files
│   └── documentation
├── Project2/
│   ├── README.md
│   ├── implementation files
│   └── documentation
└── Project3/
    ├── README.md
    ├── implementation files
    └── documentation

Key Competencies Demonstrated

• Monte Carlo simulation with variance reduction
• Finite difference PDE solvers (explicit, implicit, Crank-Nicolson)
• Tree-based methods for American options
• Multi-factor stochastic models
• Interest rate term structure modeling
• Structured product valuation
• Numerical optimization and root-finding
• Statistical analysis and result interpretation

Academic Integrity

This repository represents original academic work completed for MGMTMFE 432. The implementations follow standard financial engineering methodologies and are documented with appropriate citations where applicable.

Contact

Vikalp Thukral
UCLA Anderson School of Management
Master of Financial Engineering Program