Dynamic Futures Portfolio in a Regime-Switching Market

Regime-Switching Market

Asset prices are often seen as being dependent on market conditions. Market regimes may change suddenly and persist for a period of time. The unpredictability of the timing of regime changes also means that associated risks are almost impossible to hedge.

In order to capture these crucial properties of market dynamics, one major approach is to represent stochastic market regimes by a finite-state Markov chain. In most cases, the Markov chain is an exogenous random process and is not directly tradable. The effects of the Markov chain are reflected in the asset price dynamics. In particular, the asset’s expected return and volatility may vary across regimes.

Regime-switching time series models have been used for decades. In addition to representing asset price dynamics through changing market conditions, regime-switching models have been applied to many problems in economics and finance, including derivatives pricing and portfolio selection.

Futures Trading Problem

In our new paper, we present a stochastic control approach to generate dynamic futures trading strategies. We consider a general regime-switching framework in which the stochastic market regime is represented by a continuous-time finite-state Markov chain. The underlying asset’s spot price is modeled by a Markov modulated diffusion process.

Under the regime-switching market framework, we first derive the no-arbitrage price dynamics for the futures contracts and provide a numerical method to compute the prices.

Next, we determine the optimal futures trading strategy by solving a stochastic control problem. Our portfolio optimization approach allows for trading different numbers of futures. By analyzing and solving the associated Hamilton-Jacobi-Bellman (HJB) equations, we derive the investor’s optimal futures position over time as a function of time, spot price, and market regime.