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arXiv · 1907.12433

Algorithmic market making for options

Bastien Baldacci·Philippe Bergault·Olivier Guéant
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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.

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Bastien Baldacci, Philippe Bergault, Olivier Guéant. 2019-07-29. Algorithmic market making for options. https://arxiv.org/abs/1907.12433

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