Deep Option Pricing - Term Structure Models

Abstract

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options within the setting of interest rate term structure models. This aims to accelerate existing numerical methods which is important for applications like historical VaR or exposure calculation being used in financial institutions. With ANNs being a universal function approximation method, this method trains an ANN on synthetically generated data including term structures of yield and volatility. Then, within an VaR or exposure calculation instead of applying costly numerical methods for the financial model, the engine runs the trained ANN. This is faster and more efficient and allows (a) considering term structures of yields, (b) term structures of volatilities and (c) trade interpolation. We outline the generation of the training data, the neural net selection and propose further methods for optimization. In particular we consider a control variate method and the application of no-arbitrage conditions and regularization to the cost function used for learning and calibration. Finally, we test our approach on the Hull-White model with time-dependent term structure for volatility and the the Trolle-Schwartz model. The latter adds an un-spanned stochastic volatility to the rates dynamic. The numerical results show that the ANN solution, especially the one with the control variate, is accurate and reduces the computing time significantly.

Keywords: Machine learning, Neural networks, Computational Finance, Term Structure Models, Control Variates, Option Pricing, Hull-White model, Trolle-Schwartz Model

JEL Classification: C02, C45, G13