Algorithmic market making for options
Computational Finance
2020-07-03 v7 Mathematical Finance
Risk Management
Abstract
In this article, we tackle the problem of a market maker in charge of a book of options on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic optimal control problem of an option market maker is in fact tractable. More precisely, when volatility is modeled using a classical stochastic volatility model -- e.g. the Heston model -- the problem faced by an option market maker is characterized by a low-dimensional functional equation that can be solved numerically using a Euler scheme along with interpolation techniques, even for large portfolios. In order to illustrate our findings, numerical examples are provided.
Cite
@article{arxiv.1907.12433,
title = {Algorithmic market making for options},
author = {Bastien Baldacci and Philippe Bergault and Olivier Guéant},
journal= {arXiv preprint arXiv:1907.12433},
year = {2020}
}