Pricing options and computing implied volatilities using neural networks

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent's iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly

Option Pricing: The empirical tests of the Black-Scholes pricing formula and the feed-forward networks

In this article we evaluate the pricing performance of the rather simple but revolutionary Black-Scholes model and one of the more complex techniques (neural networks) on the European-style S&P Index call and put options over the period of 1.6.2006 till 8.6.2007. Our results on call options show that generally Black-Scholes model performs better than simple generalized feed-forward networks. On the other hand neural networks performance is improving as the option goes deep in the money and as days to expiration increase, compared to the worsening performance of the BS models. Neural networks seem to correct for the well-known Black-Scholes model moneyness and maturity biases.option pricing, neural networks

A machine learning approach to portfolio pricing and risk management for high-dimensional problems

We present a general framework for portfolio risk management in discrete time, based on a replicating martingale. This martingale is learned from a finite sample in a supervised setting. The model learns the features necessary for an effective low-dimensional representation, overcoming the curse of dimensionality common to function approximation in high-dimensional spaces. We show results based on polynomial and neural network bases. Both offer superior results to naive Monte Carlo methods and other existing methods like least-squares Monte Carlo and replicating portfolios.Comment: 30 pages (main), 10 pages (appendix), 3 figures, 22 table

Combining domain knowledge and statistical models in time series analysis

This paper describes a new approach to time series modeling that combines subject-matter knowledge of the system dynamics with statistical techniques in time series analysis and regression. Applications to American option pricing and the Canadian lynx data are given to illustrate this approach.Comment: Published at http://dx.doi.org/10.1214/074921706000001049 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

MQLV: Optimal Policy of Money Management in Retail Banking with Q-Learning

Reinforcement learning has become one of the best approach to train a computer game emulator capable of human level performance. In a reinforcement learning approach, an optimal value function is learned across a set of actions, or decisions, that leads to a set of states giving different rewards, with the objective to maximize the overall reward. A policy assigns to each state-action pairs an expected return. We call an optimal policy a policy for which the value function is optimal. QLBS, Q-Learner in the Black-Scholes(-Merton) Worlds, applies the reinforcement learning concepts, and noticeably, the popular Q-learning algorithm, to the financial stochastic model of Black, Scholes and Merton. It is, however, specifically optimized for the geometric Brownian motion and the vanilla options. Its range of application is, therefore, limited to vanilla option pricing within financial markets. We propose MQLV, Modified Q-Learner for the Vasicek model, a new reinforcement learning approach that determines the optimal policy of money management based on the aggregated financial transactions of the clients. It unlocks new frontiers to establish personalized credit card limits or to fulfill bank loan applications, targeting the retail banking industry. MQLV extends the simulation to mean reverting stochastic diffusion processes and it uses a digital function, a Heaviside step function expressed in its discrete form, to estimate the probability of a future event such as a payment default. In our experiments, we first show the similarities between a set of historical financial transactions and Vasicek generated transactions and, then, we underline the potential of MQLV on generated Monte Carlo simulations. Finally, MQLV is the first Q-learning Vasicek-based methodology addressing transparent decision making processes in retail banking