Optimal Trading in Commodity Markets: A Stochastic Optimal Control Approach under Transaction Costs, Predictable Returns, and Stochastic Volatility

Abstract

This thesis studies an optimal trading problem for commodities under predictable returns, transaction costs, and stochastic volatility. Extending the work of Chan, Sircar, and Zimbidis in equities, I adapt the model to a commodity setting by introducing price dynamics via the two-factor Schwartz model. This modification makes the associated Hamilton-Jacobi-Bellman equation nonlinear, so the problem is no longer tractable in closed form. I formulate the problem in a stochastic optimal control framework and reduce the HJB equation through a quadratic ansatz in the inventory variable. The resulting system is solved numerically to converge to the viscosity solution of the HJB using a finite-difference scheme with backward Euler time stepping and upwind discretization. I then use Monte Carlo simulation to evaluate the performance of the strategy. In the empirical implementation, I calibrate a reduced one-factor stochastic-volatility model using WTI crude oil market data and the OVX volatility index. The numerical results indicate that stochastic volatility materially affects the optimal trading strategy. Compared to a constant-volatility benchmark, the stochastic-volatility strategy delivers higher expected profit and loss, but also a wider distribution of outcomes with positive skewness. The code and data may be accessed in GitHub: https://github.com/aidenkaufman/Senior_Thesis/tree/main.