Inventory Hedging And Option Market Making

In this paper, we develop an inventory-based approach to analyze the option market making activity. Indeed, we formulate and analytically solve the price-setting problem of a monopolistic option market maker facing exogenous public supply and demand first on a single exercise price (the "single option economy") and next on multiple exercise prices (the "multi-options economy"). While in the "single option economy" the familiar result that market maker inventory and price level are inversely related holds, the same is not necessarily true in the "multi-options economy". Additionally, we examine under which theoretical condition hedging is totally effective (i.e., the variance of the market maker hedged position is zero). Last but not least, our model is fully consistent with actual option market making practices, which consist in trading hedge portfolios to reduce risk. As such, our approach can be considered as a bridge between market microstructure and standard option pricing literature.