Mean-Variance Hedging with Uncertain Trade Execution

Abstract

This paper studies a hedging problem of a contingent claim in a discrete time model. The contingent claim is hedged by one illiquid risky asset and the hedging error is measured by a quadratic criterion. In our model, trade does not always succeed and then trade times are not only discrete, but also random. The uncertainty of trade execution represents the liquidity risk. First we find an optimal hedging strategy with fixed initial condition. Next we consider an optimal initial condition. Finally, we study a binomial model as a simple example.

Key Words:

• Hedging
• derivatives
• execution risk

Acknowledgements

I would like to dedicate this paper to my late father, Takeo Matsumoto. I wish to thank Professor Shigeo Kusuoka for helpful discussions and comments. I thank the participants of the Workshop and Mid Term Conference on Advanced Mathematical Methods for Finance, for their valuable comments. I am grateful to an anonymous referee for assistance in revising the paper. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B), 19740051.