Time- and State-Dependent Resampling

28 Pages Posted: 24 Feb 2025 Last revised: 4 Mar 2025

See all articles by Laura Kristensen

Laura Kristensen

Fortitudo Technologies

Anton Vorobets

Fortitudo Technologies

Date Written: January 30, 2025

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

Suggested Citation

Kristensen, Laura and Vorobets, Anton, Time- and State-Dependent Resampling (January 30, 2025). Available at SSRN: https://ssrn.com/abstract=5117589 or http://dx.doi.org/10.2139/ssrn.5117589

Laura Kristensen

Fortitudo Technologies ( email )

Østre Stationsvej 39B, 8. th.
Odense C, 5000
Denmark

HOME PAGE: http://fortitudo.tech

Anton Vorobets (Contact Author)

Fortitudo Technologies ( email )

Østre Stationsvej 39B, 8. th.
Odense C, 5000
Denmark

HOME PAGE: http://fortitudo.tech

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