ESSAYS IN MATHEMATICAL FINANCE AND MACHINE LEARNING
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This dissertation consists of three independent essays. Chapter 1, “Exploring Machine Learning in Fixed Income Market” designs a decision support framework that can be used to provide suggested indications of future U.S. on-the-run 10Y Treasury market direction along with the associated probability of making that move. My primary innovation is proposing a framework for applying machine learning methods to U.S. fixed income market. The framework includes a newly proposed performance metric that combines profitability and randomness to select proper outperform models and a sliding window cross-validation method for streaming data learning. I find the Random Forest method provides a decent Sharpe ratio for trading U.S. 10Y Treasury in a “quarantined” testing set but underperforms on Spread trading (10Y Treasury and an asset swap) and Volatility trading (1M10Y Swaption Straddle). Chapter 2, “A Robust Trend Following Framework: Theory and Application” constructs a trend-following signal based on statistical theory and analytically analyzes its properties. I manage to reconcile our model's theoretical results with stylized facts about trend-following investing – the presence of a "CTA smile". Leveraging on the theoretical results, we proposed a prototype trend-following framework that is diversified across time-frames and assets. I also discuss the portfolio and risk management of the trend-following strategy. I illustrate the risk-budgeting approach can be used to enhance the trend-following framework. Different approaches to control the costs have also been discussed. Chapter 3, “Markov Modulated Bilateral Gamm Mean Reversion Model” proposed a Markov modulated Bilateral gamma mean-reversion model. Market practitioners argue the market has high volatility regimes and low volatility regimes. I argue the model can capture the mean reversion, asymmetries of returns of up moves and down moves, and other empirical regularities. I derived the characteristic function and provide preliminary parameter estimates by calibrating the model to VIX Index upon the assumption of stationary distribution to avoid using filter methodologies.