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A novel generative machine learning approach for the simulation of sequencesof financial price data with drawdowns quantifiably close to empirical data isintroduced. Applications such as pricing drawdown insurance options ordeveloping portfolio drawdown control strategies call for a host ofdrawdown-realistic paths. Historical scenarios may be insufficient toeffectively train and backtest the strategy, while standard parametric MonteCarlo does not adequately preserve drawdowns. We advocate a non-parametricMonte Carlo approach combining a variational autoencoder generative model witha drawdown reconstruction loss function. To overcome issues of numericalcomplexity and non-differentiability, we approximate drawdown as a linearfunction of the moments of the path, known in the literature as pathsignatures. We prove the required regularity of drawdown function andconsistency of the approximation. Furthermore, we obtain close numericalapproximations using linear regression for fractional Brownian and empiricaldata. We argue that linear combinations of the moments of a path yield amathematically non-trivial smoothing of the drawdown function, which gives oneleeway to simulate drawdown-realistic price paths by including drawdownevaluation metrics in the learning objective. We conclude with numericalexperiments on mixed equity, bond, real estate and commodity portfolios andobtain a host of drawdown-realistic paths.

Generating drawdown-realistic financial price paths using path signatures