2019/07/29 by Bastien Baldacci, Baldacci, Bastien, Philippe Bergault +3 · 1 citation
Economics, Econometrics and Finance · Social Sciences · #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Risk Management (q-fin.RM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1907.12433
openalex publication_date 2019/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.