Machine Learning-powered Pricing of the Multidimensional Passport Option

TL;DR

This paper develops a discrete-time solution for multidimensional Black-Scholes markets and introduces machine learning methods, including deep reinforcement learning, to price complex options like the passport option in multi-asset settings.

Contribution

It provides the first discrete-time solution for multi-dimensional uncorrelated Black-Scholes markets and introduces novel machine learning approaches for pricing multidimensional options.

Findings

Successful pricing of passport options in uncorrelated Black-Scholes markets.

Demonstrated effectiveness of machine learning methods for multidimensional option pricing.

Extended pricing techniques to multi-asset, multi-dimensional market models.

Abstract

Introduced in the late 90s, the passport option gives its holder the right to trade in a market and receive any positive gain in the resulting traded account at maturity. Pricing the option amounts to solving a stochastic control problem that for $d>1$ risky assets remains an open problem. Even in a correlated Black-Scholes (BS) market with $d=2$ risky assets, no optimal trading strategy has been derived in closed form. In this paper, we derive a discrete-time solution for multi-dimensional BS markets with uncorrelated assets. Moreover, inspired by the success of deep reinforcement learning in, e.g., board games, we propose two machine learning-powered approaches to pricing general options on a portfolio value in general markets. These approaches prove to be successful for pricing the passport option in one-dimensional and multi-dimensional uncorrelated BS markets.