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Liquidity costs: a new numerical methodology and an empirical study

Christophe Michel 1 Victor Reutenauer 2 Denis Talay 3 Etienne Tanré 3
3 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : We consider rate swaps which pay a fixed rate against a floating rate in presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit optimal strategy minimizing a risk measure of the hedging error. We here propose an efficient algorithm, based on the stochas-tic gradient method, to obtain an approximate optimal strategy without solving a stochastic control problem. We validate our algorithm by numer-ical experiments. We also develop several variants of the algorithm and discuss their performances in terms of the numerical parameters and the liquidity cost.
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Christophe Michel, Victor Reutenauer, Denis Talay, Etienne Tanré. Liquidity costs: a new numerical methodology and an empirical study. Applied Mathematical Finance, Taylor & Francis (Routledge): SSH Titles, 2016, ⟨10.1080/1350486X.2016.1164608⟩. ⟨hal-01098096v3⟩

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