Foreign exchange trading and management with the stochastic dual dynamic programming method

We present a novel tool for generating speculative and hedging foreign exchange (FX) trading policies. Our solution provides a schedule that determines trades in each rebalancing period based on future currency prices, net foreign account positions, and incoming (outgoing) flows from business operations. To obtain such policies, we construct a multistage stochastic programming (MSP) model and solve it using the stochastic dual dynamic programming (SDDP) numerical method, which specializes in solving high-dimensional MSP models. We construct our methodology within an open-source SDDP package, avoiding implementing the method from scratch. To measure the performance of our policies, we model FX prices as a mean-reverting stochastic process with random events that incorporate stochastic trends. We calibrate this price model on seven currency pairs, demonstrating that our trading policies not only outperform the benchmarks for each currency, but may also be close to ex-post optimal solutions. We also show how the tool can be used to generate more or less conservative strategies by adjusting the risk tolerance, and how it can be used in a variety of contexts and time scales, ranging from intraday speculative trading to monthly hedging for business operations. Finally, we examine the impact of increasing trade policy uncertainty (TPU) levels on our findings. Our findings show that the volatility of currencies from emerging economies rises in comparison to currencies from developed markets. We discover that an increase in the TPU level has no effect on the average profit obtained by our method. However, the risk exposure of the policies increases (decreases) for the group of currencies from emerging (developed) markets.