Dynamic Mis-Specification in Local-Stochastic Volatility Models

13 Pages Posted: 8 May 2009 Last revised: 1 Jun 2009

Date Written: May 5, 2009

Abstract

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.

Keywords: Replication error, model selection, local and stochastic volatility modelling, implied stochastic volatility

Suggested Citation

Di Graziano, Giuseppe and Galluccio, Stefano, Dynamic Mis-Specification in Local-Stochastic Volatility Models (May 5, 2009). Available at SSRN: https://ssrn.com/abstract=1399603 or http://dx.doi.org/10.2139/ssrn.1399603

Giuseppe Di Graziano

J.P. Morgan Chase & Co. ( email )

60 Wall St.
New York, NY 10260
United States

Stefano Galluccio (Contact Author)

BNP Paribas Fixed Income ( email )

10, Harewood Avenue
NW1 6AA London
United Kingdom

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