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 .
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 .
R
equity derivatives
options
D
equity
A
when volatility is modeled using a classical stochastic volatility model -- e.g. the Heston model --
D
equity
R
two-dimensional
low-dimensional
R
interpolation techniques and classical Euler schemes
a Euler scheme along with interpolation techniques
R
Numerical
In order to illustrate our findings, numerical
D
for a large book of equity options