A Tractable Framework for Option Pricing with Dynamic Market Maker Inventory and Wealth

We develop a tractable dynamic model of an index option market maker with limited capital and characterize how option prices depend on inventory risk and market maker wealth. The risk averse market maker absorbs positive demand by end users and requires a more negative variance risk premium when she incurs losses. The model is parsimonious and nests existing reduced-form stochastic-volatility models. We estimate the model using returns, options, and inventory and find that it performs well, especially during the financial crisis. The restrictions imposed by existing stochastic-volatility models are strongly rejected in favor of the model with a market maker