Pricing and hedging American-style options with deep learning

Abstract

In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a point estimate and confidence intervals. Finally, it constructs an approximate dynamic hedging strategy. We test the approach on different specifications of a Bermudan max-call option. In all cases it produces highly accurate prices and dynamic hedging strategies with small replication errors.

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• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options
• Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions

Cited by in corpus (7)

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• Solving high-dimensional optimal stopping problems using deep learning
• Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations
• Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing
• Solving optimal stopping problems with Deep Q-Learning
• Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks
• Machine-learning regression methods for American-style path-dependent contracts