In this article, we tackle the problem of a market maker in charge of a book of equity derivatives 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 equity option market maker is in fact tractable. More precisely, the problem faced by an equity option market maker is characterized by a two-dimensional functional equation that can be solved numerically using interpolation techniques and classical Euler schemes, even for large portfolios. Numerical examples are provided for a large book of equity options.
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