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Liquidity costs: a new numerical methodology and an empirical study

Author

Listed:
  • Christophe Michel

    (FIM - Service Interest Rates and Hybrid Quantitative Research - CALYON)

  • Victor Reutenauer

    (Fotonower)

  • Denis Talay

    (TOSCA - TO Simulate and CAlibrate stochastic models - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique)

  • Etienne Tanré

    (TOSCA - TO Simulate and CAlibrate stochastic models - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Christophe Michel & Victor Reutenauer & Denis Talay & Etienne Tanré, 2016. "Liquidity costs: a new numerical methodology and an empirical study," Post-Print hal-01098096, HAL.
    • Handle: RePEc:hal:journl:hal-01098096
    DOI: 10.1080/1350486X.2016.1164608
    Note: View the original document on HAL open archive server: https://inria.hal.science/hal-01098096v3
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    References listed on IDEAS

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    4. Gibson, Rajna & Lhabitant, Francois-Serge & Talay, Denis, 2010. "Modeling the Term Structure of Interest Rates: A Review of the Literature," Foundations and Trends(R) in Finance, now publishers, vol. 5(1–2), pages 1-156, December.
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    Keywords

    Optimization optimisation; Stochastic Algorithms; Interest rates derivatives;
    All these keywords.

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