Applied Math Seminar
Title: A Simple Probabilistic Representation of an Arbitrage-free Implied Variance Rate Smile
Speaker: Peter Carr, NYU
Date: December 6, 2017
Location: Building 380
When the variance rates implied from option prices differ across strike prices, at most one of them can be interpreted as the variance rate of the underlying security price. We develop an arbitrage-free option pricing model with four stochastic state variables, one of which is the underlying security price. We show how to successively explicitly determine the other three state variables from three given co-terminal arbitrage-free implied variance rates. The resulting calibrated implied variance rate smile is given a simple probabilistic representation. To our knowledge, this is the first non-flat implied variance rate smile enjoying any probabilistic interpretation.