Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model

TL;DR

This paper develops numerical methods for pricing exchange options in markets with finite liquidity, incorporating price impact, and introduces a deep learning framework for practical implementation.

Contribution

It introduces a novel numerical pricing approach for exchange options considering market liquidity and price impact, along with a deep learning implementation framework.

Findings

Effective two-dimensional Milstein scheme for asset simulation

Monte Carlo method with Margrabe option as controlled variate

Deep learning framework for real-world application

Abstract

In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading in our market model has a direct impact on the asset's price. The price impact is incorporated into the dynamics of the first asset through a specific trading strategy, as in large trader liquidity model. Two-dimensional Milstein scheme is implemented to simulate the pair of assets prices. The option value is numerically estimated by Monte Carlo with the Margrabe option as controlled variate. Time complexity of these numerical schemes are included. Finally, we provide a deep learning framework to implement this model effectively in a production environment.