Liquidity Costs: A New Numerical Methodology and an Empirical Study. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Michel, Christophe; Reutenauer, Victor; Talay, Denis; Tanré, Etienne
• Is Part Of: Applied mathematical finance. Volume 23:Issue 1(2016)
• Page Start: 57
• Page End: 79
• Publication Date: 2016-01-02
• Subjects: Interest rate derivatives -- optimization -- stochastic algorithms; Business mathematics -- Periodicals; 650.0151
• DOI: 10.1080/1350486X.2016.1164608
• Languages: English
• ISSNs: 1350-486X

Abstract

ABSTRACT: We consider rate swaps which pay a fixed rate against a floating rate in the presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit strategy optimizing an expected function of the hedging error. We here propose an efficient algorithm based on the stochastic gradient method to compute an approximate optimal strategy without solving a stochastic control problem. We validate our algorithm by numerical experiments. We also develop several variants of the algorithm and discuss their performances in terms of the numerical parameters and the liquidity cost.