Dynamic Mis-Specification in Local-Stochastic Volatility Models

In the context of interest rate derivatives, we present two simple cases of replication error associated with common hedging strategies when agents have partial information about the real dynamics of the underlying asset. In particular, we derive an explicit expression for the hedging error due to model mis-specification in the following cases, i) the trader delta-hedges his option position in the Black and Scholes framework with stochastic implied volatilities, and ii) the trader uses a given local-stochastic volatility model to delta and vega hedge his/her option exposure but the real dynamics of the underlying follow a different local-stochastic volatility process