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Subject: deep learning × WGL Institute: WIAS ×

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    Optimal stopping via deeply boosted backward regression
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Belomestny, Denis; Schoenmakers, John G.M.; Spokoiny, Vladimir; Tavyrikov, Yuri
    In this note we propose a new approach towards solving numerically optimal stopping problems via boosted regression based Monte Carlo algorithms. The main idea of the method is to boost standard linear regression algorithms in each backward induction step by adding new basis functions based on previously estimated continuation values. The proposed methodology is illustrated by several numerical examples from finance.
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    Deep calibration of rough stochastic volatility models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Bayer, Christian; Stemper, Benjamin
    Sparked by Alòs, León und Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson und Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz und Gatheral (2016) constitute the latest evolution in option price modeling. Unlike standard bivariate diffusion models such as Heston (1993), these non-Markovian models with fractional volatility drivers allow to parsimoniously recover key stylized facts of market implied volatility surfaces such as the exploding power-law behaviour of the at-the-money volatility skew as time to maturity goes to zero. Standard model calibration routines rely on the repetitive evaluation of the map from model parameters to Black-Scholes implied volatility, rendering calibration of many (rough) stochastic volatility models prohibitively expensive since there the map can often only be approximated by costly Monte Carlo (MC) simulations (Bennedsen, Lunde & Pakkanen, 2017; McCrickerd & Pakkanen, 2018; Bayer et al., 2016; Horvath, Jacquier & Muguruza, 2017). As a remedy, we propose to combine a standard Levenberg-Marquardt calibration routine with neural network regression, replacing expensive MC simulations with cheap forward runs of a neural network trained to approximate the implied volatility map. Numerical experiments confirm the high accuracy and speed of our approach.