Portfolio

Kalman Filter Estimation for Cox-Ingersoll-Ross Term Structure Model [PDF] [Github]

The Cox-Ingersoll-Ross (CIR) model is a mathematical model that assumes interest rates will go back to a long-term average, which helps explain why interest rates usually stay positive in the real world. This makes the CIR model useful for understanding how interest rates change in financial markets. However, real-world data is often noisy and not always perfect. This is where the Kalman filter comes in. It is an algorithm that helps estimate the true values of a system by predicting, updating, and correcting guesses as new data is added. When used with the CIR model, the Kalman filter helps improve the accuracy of interest rate predictions by removing unnecessary noise and focusing on the important information.

Maximal Central Differencing Optimal Portfolio Selection for Power Utility [PDF] [Github]

This paper introduces a numerical method for solving the optimal portfolio selection problem in a financial market with two assets: a risk-free bond and a risky stock. The goal is to find an investment strategy that maximizes the expected utility of terminal wealth. The problem is modeled as a stochastic differential equation, which describes the evolution of the wealth process over time. The solution is approached by solving the Hamilton-Jacobi-Bellman equation using a finite difference scheme, where both the state and time are discretized. Central differencing is used for most terms, with forward and backward differencing applied where necessary to maintain stability.

Numerical Scheme for the Optimal Stopping Problem for Pairs Trading [PDF] [Github]

This project focuses on modeling an investor’s decision regarding the optimal time to liquidate a position in a pairs trading portfolio. The strategy involves taking a long position in one stock and an offsetting short position in a cointegrated stock, resulting in a wealth process that is stationary. Assuming the wealth process exhibits a finite number of jumps, the objective is to determine the optimal stopping time for liquidation. To address the challenge of evaluating this stopping time, numerical methods such as finite differences and quadrature were employed to solve the associated differential equation.

Other Projects

1. Deep BSDE Notes [PDF] - This is a set of notes I wrote to help myself understand how deep learning can be used to solve backward stochastic differential equations (BSDEs), which are closely tied to certain nonlinear partial differential equations. I start by reviewing the basic theory behind SDEs, BSDEs, and their connection to PDEs, then explore how neural networks can approximate solutions in high dimensions.
   
   2. Computational Finance Repository [Github] - This repository contains a set of Jupyter notebooks focused on key methods in computational finance, particularly option pricing. It includes implementations of Monte Carlo simulations for pricing and updating results, Fourier-based approaches such as the COS method and FFT for density recovery and derivative valuation, and simulations of stochastic processes like Geometric Brownian Motion and correlated Brownian motions. The collection also covers the estimation of implied volatility
   
   3. Fundamental Analysis [PDF] - While most of my recent work has been on quantitative finance, I’m also familiar with traditional financial methodologies. This project is an analysis of corporate governance, historical risk and return, capital structure, company project characteristics, and dividend policy to provide a valuation and recommendations for each company.