Algorithmic market making for options

Bastien Baldacci, Philippe Bergault and Olivier Guéant

Quantitative Finance, 2021, vol. 21, issue 1, 85-97

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.

Date: 2021
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DOI: 10.1080/14697688.2020.1766099

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