Projects

A generated map of long-running projects, related series, and standalone notes.

Projects marked as Work in Progress (WIP) are still in progress and may not be fully functional.

1 Volatility Forecasting

My work on volatility forecasting. How far can we go by extending a simple exponential smoothing filter?

Volatility Forecasts (Part 1 - STES Model): Exponential smoothing (ES) is a simple yet widely used approach to volatility forecasting in finance and economics.
Volatility Forecasts (Part 2 - XGBSTES Algorithm 1): In the previous post, we replicated the Smooth Transition Exponential Smoothing (STES) model from (Taylor 2004) and (Liu, Taylor, Choo 2020).
Volatility Forecasts (Part 3 - XGBSTES Algorithm 2): We extend STES by replacing its linear component with XGBoost, then dig into why RMSE can underperform and propose a more stable end-to-end fitting algorithm.
Volatility Forecasts (Part 4 — RMSE Benchmarks and QLIKE Training): We keep RMSE for benchmark comparability, then refit STES and XGBSTES under QLIKE to see how the training loss changes out-of-sample ranking and calibration.
Volatility Forecasts (Part 5 — PGARCH): Part 5 revisits the three-feature PGARCH stage: with only fast return features, a dynamic long-run anchor is hard to interpret, so the cleaner specification keeps mu constant and lets persistence and shock loading adapt.
Signature Methods (Part 4 — Rolling Signatures in Volatility Forecasts): We augment STES and XGBoost-STES volatility models with rolling signature features computed from SPY return paths. After careful feature selection, regularization tuning, and multi-channel augmentation, we conclude that the results are negative but instructive.

My study notes on the signature method.

Signature Methods (Part 1 - Motivation): I am starting a series on the signature method now that I have some free time on my hands over the 2025 holiday season.
Signature Methods (Part 2 - Signature and Augmentation): Previously I provided some motivations for the use of signatures.
Signature Methods (Part 3 - Lead–Lag Augmentation and Practical Limitations to the Signature Method): Continuing from the previous post, we work through three examples of approximating path functionals using linear functionals of truncated signatures in increasingly less practical way to illustrate…
Signature Methods (Part 4 — Rolling Signatures in Volatility Forecasts): We augment STES and XGBoost-STES volatility models with rolling signature features computed from SPY return paths. After careful feature selection, regularization tuning, and multi-channel augmentation, we conclude that the results are negative but instructive.

A long-running refresher series on short-rate and term-structure models.

Short Rate Models (Part 1: Introducing Merton’s Model): Welcome to my refresher series on short-rate models, dear reader! These mathematical marvels are not just academic curiosities but crucial tools in finance.
Short Rate Models (Part 2: Simulating and Calibrating the Merton Model): Let us continue our refresher series on short-rate models. We introduced the Merton short rate model in the previous post.
Short Rate Models (Part 3: Introducing Vasicek Model): We continue our refresher series on the short-rate models. In the previous post, I introduced the Merton model and the Euler-Maruyama method to simulate it.
Short Rate Models (Part 4: Simulating and Calibrating the Vasicek Model): In our previous post, we introduced the Vasicek model that used the Ornstein-Uhlenbeck (OU) process to model the dynamics of the short rates.

Analytical notes on the expected performance of mean-reversion trading strategies under progressively more realistic assumptions.

Expected Performance of a Mean-Reversion Trading Strategy - Part 1: A value strategy posits that the worth of an asset tends to oscillate around a more gradual, underlying trend.
Expected Performance of a Mean-Reversion Trading Strategy - Part 2: What happens to the performance of a mean-reversion strategy when the fair value is estimated with a constant bias?
Expected Performance of a Mean-Reversion Trading Strategy - Part 3: How does a correlated bias in the fair-value estimate affect the Sharpe ratio of a mean-reversion strategy?
Expected Performance of a Mean-Reversion Trading Strategy — Part 4: How does parameter estimation error affect the Sharpe ratio of a mean-reversion strategy?

My capstone project for the Applied Data Science certificate program with MIT Professional Education.

Malaria Detection (Part 1: Introduction and Data Preparation): I recently learned more about convolutional neural networks (CNNs) and how they are used to analyze images.
Malaria Detection (Part 2: Model Building and Training): In the previous post of this series, we introduced the problem of Malaria detection and prepared and preprocessed our dataset.
Malaria Detection (Part 3: Results and Reflections): I was honestly amazed by these results. Even the base model achieved 98% accuracy! However, accuracy isn’t everything. Let’s break down what these numbers really mean.
Malaria Detection (Part 4: Finetuning VGG16 with LoRA): In the previous post, we built a finetuned VGG16-based model (Model 4) to detect malaria from cell images.

Notes and experiments on graph-regularized low-rank models and related dimensionality-reduction ideas.

A step-by-step guide to implementing nowcasting models based on dynamic factor models in Python.

Writing for this project is not published yet.

Notes and future videos on mathematical ideas I have been teaching my kids.

Writing for this project is not published yet.