# Algorithmic market making for options

## TL;DR

This paper develops a tractable approach for optimal market making in options by reducing a high-dimensional control problem to a low-dimensional one using vega approximation, enabling efficient numerical solutions.

## Contribution

It introduces a novel method to simplify the complex stochastic control problem of options market making into a low-dimensional equation using vega approximation, applicable to models like Heston.

## Key findings

- The method simplifies high-dimensional control problems to low-dimensional equations.
- Numerical solutions are feasible using Euler schemes and interpolation.
- The approach is demonstrated with numerical examples.

## 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.