Evaluating discrete dynamic strategies in affine models

Abstract

We consider the problem of measuring the performance of a dynamic strategy, re-balanced at a discrete set of dates, with the objective of hedging a claim in an incomplete market driven by a general multi-dimensional affine process. The main purpose of the paper is to propose a method to efficiently compute the expected value and variance of the hedging error of the strategy. Representing the payoff of the claim as an inverse Laplace transform, we are able to obtain semi-explicit formulas for strategies satisfying a certain property. The result is quite general and can be applied to a very rich class of models and strategies, including Delta hedging. We provide illustrations for the case of the Heston stochastic volatility model.

• Hedging errors
• Trading strategies
• Incomplete markets
• Multi-factor models
• Derivatives hedging

JEL Classification:

• C0
• C00
• C6
• C60

Acknowledgements

The financial support of the Research Grant: PRIN 2008, Probability and finance, Prot. 2008YYYBE4, is gratefully acknowledged. We would also like to thank Damir Filipović for many helpful comments.

Notes

†We mention that an approach present in the literature is to compute hedging errors under the risk-neutral probability, in other words when the model is calibrated on market prices (see, e.g., Denkl et al. (2011) and references therein).

‡This is sometimes called the moment generating function, but here we adopt the terminology used by Duffie et al. (2003) and Filipović (2009).

†In Glasserman and Kim (2010) there is a typo for this case.