This was part of Dynamic Assessment Indices
Convex measures of model risk for option hedging and nonlinear Black Scholes equations
Rüdiger Frey, Vienna University of Economics and Business
Wednesday, May 11, 2022
Abstract: In this talk we discuss the dual representation for measures of the model risk in option hedging that is due to market `frictions’ such as illiquid markets or stochastic volatility . Starting point is the observation that superhedging prices for options in the presence of market frictions can be described by nonlinear versions of the classical Black Scholes equation. We apply duality theory to show that this equation can be interpreted as a dynamic programming equation and we discuss existence and comparison principles. We show that the superhedging price gives rise to a convex risk measure on the set of all continuous terminal value claims whose dual representation has a very intuitive interpretation. We consider next asymptotic properties of this measure as market frictions get large. Finally we propose an approach for discussing the pricing of individual contracts relative to a book of derivatives and we discuss open research questions.