We propose a neural network approach to price EU call options that significantly outperforms some existing pricing models and comes with guarantees that its predictions are economically reasonable. To achieve this, we introduce a class of gated neural networks that automatically learn to divide-and-conquer the problem space for robust and accurate pricing. We then derive instantiations of these networks that are 'rational by design' in terms of naturally encoding a valid call option surface that enforces no arbitrage principles. This integration of human insight within data-driven learning provides significantly better generalisation in pricing performance due to the encoded inductive bias in the learning, guarantees sanity in the model's predictions, and provides econometrically useful byproduct such as risk neutral density.
Learning from demonstration has been widely studied in machine learning but becomes challenging when the demonstrated trajectories are unstructured and follow different objectives. This short-paper proposes PODNet, Plannable Option Discovery Network, addressing how to segment an unstructured set of demonstrated trajectories for option discovery. This enables learning from demonstration to perform multiple tasks and plan high-level trajectories based on the discovered option labels. PODNet combines a custom categorical variational autoencoder, a recurrent option inference network, option-conditioned policy network, and option dynamics model in an end-to-end learning architecture. Due to the concurrently trained option-conditioned policy network and option dynamics model, the proposed architecture has implications in multi-task and hierarchical learning, explainable and interpretable artificial intelligence, and applications where the agent is required to learn only from observations.
We propose a deep neural network framework for computing prices and deltas of American options in high dimensions. The architecture of the framework is a sequence of neural networks, where each network learns the difference of the price functions between adjacent timesteps. We introduce the least squares residual of the associated backward stochastic differential equation as the loss function. Our proposed framework yields prices and deltas on the entire spacetime, not only at a given point. The computational cost of the proposed approach is quadratic in dimension, which addresses the curse of dimensionality issue that state-of-the-art approaches suffer. Our numerical simulations demonstrate these contributions, and show that the proposed neural network framework outperforms state-of-the-art approaches in high dimensions.
This paper shows how the prices of option contracts traded in financial marketscan be tracked sequentially by means of the Extended Kalman Filter algorithm. I consider call and put option pairs with identical strike price and time of maturity as a two output nonlinear system.The Black-Scholes approach popular in Finance literature andthe Radial Basis Functions neural network are used in modelling the nonlinear system generating these observations. I show how both these systems may be identified recursively using the EKF algorithm. I present results of simulations on some FTSE 100 Index options data and discuss the implications of viewing the pricing problem in this sequential manner. 1 INTRODUCTION Data from the financial markets has recently been of much interest to the neural computing community. The complexity of the underlying macroeconomic system and how traders react to the flow of information leads to highly nonlinear relationships betweenobservations.
We not only tackle the theory but give practical guidance and live demonstrations of the computational methods involved. After introducing the subject we cover Gaussian Process Regression and Artificial Neural Networks and show how such methods can be applied to solve option pricing problems, speed up the calculation of xVAs or apply them for hedging. We further show how to use existing pricing libraries to interact with machine learning environments often set up in Python. We explain how to set up the methods mainly in Python using Keras, Tensorflow or SciKit Learn. We give many examples which are directly related to financial mathematics and can be explored further after the course.