Option Replication in Discrete Time with Illiquidity

Abstract

This article studies a replication of a contingent claim in an illiquid market. We represent the liquidity as a supply curve in a discrete time model. Because the trade price of the illiquid asset is a function of the trade size in this model, it is important whether the contingent claim is physically settled or settled in cash. In both cases, we give a condition where a replication strategy exists uniquely and show some properties of the replication strategy. Further we analyse the liquidity cost numerically.

Key Words:

• replication
• supply curve
• settlement method

Acknowledgements

I thank the participants of Quantitative Methods in Finance Conference 2009, for their valuable comments. I also thank the anonymous referee for assistance in revising the article. This research was partially supported by the Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Young Scientists (B), 19740051, 23740080.