Time- and State-Dependent Resampling

Abstract

This article introduces Time-and State-Dependent Resampling methods that allow us to perform resampling of historical investment time series to generate new synthetic paths conditional on arbitrarily complex state variables and time decay. The article also presents a mathematical analysis of the Fully Flexible Resampling (FFR) method, which is an instance of the new resampling class recently introduced in the Portfolio Construction and Risk Management book. We prove that the new approach generates stationary simulations while giving us additional flexibility to capture the time series dependencies compared to other traditional resampling methods. The case study illustrates that the FFR method also allows us to perform state variable stress-testing, for example, assessing the effect of a sudden volatility spike on various time horizons. The appendices contain all the necessary proofs for the new class of Time- and State-Dependent Resampling methods.

Documented Python code that replicates the results of the case study is available in the open-source package fortitudo.tech. More information about the package can be found on https://os.fortitudo.tech.

Keywords: Time-and State-Dependent Resampling, Fully Flexible Resampling, Markov chain, Markov chain Monte Carlo, Monte Carlo simulation, market simulation, synthetic market data, Entropy Pooling, relative entropy, Kullback-Leibler divergence, stationary transformations, Python Programming Language