Optimal Option Market Making and Volatility Arbitrage

Abstract

We introduce a market making model of options which can encompass the trader's view on the underlying volatility versus the market implied volatility surface. An approximately optimal strategy is derived in closed form, where the optimal bid and ask levels depend on the expected volatility arbitrage profits associated with the quoted options. We show that the model can be extended to include additional features such as trading position limit, market making of arbitrary European derivatives, simultaneous market making of multiple options, and incorporation of risk control over customised factors.

Keywords: Market making, algorithmic trading, options, volatility arbitrage, Hamilton–Jacobi–Bellman equation

JEL Classification: C61, D40, G12