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European Option Pricing with Liquidity Shocks

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  • Michael Ludkovski
  • Qunying Shen

Abstract

We study the valuation and hedging problem of European options in a market subject to liquidity shocks. Working within a Markovian regime-switching setting, we model illiquidity as the inability to trade. To isolate the impact of such liquidity constraints, we focus on the case where the market is completely static in the illiquid regime. We then consider derivative pricing using either equivalent martingale measures or exponential indifference mechanisms. Our main results concern the analysis of the semi-linear coupled HJB equation satisfied by the indifference price, as well as its asymptotics when the probability of a liquidity shock is small. We then present several numerical studies of the liquidity risk premia obtained in our models leading to practical guidelines on how to adjust for liquidity risk in option valuation and hedging.

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  • Michael Ludkovski & Qunying Shen, 2012. "European Option Pricing with Liquidity Shocks," Papers 1205.1007, arXiv.org.
    • Handle: RePEc:arx:papers:1205.1007
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    References listed on IDEAS

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    7. Schwartz, Eduardo S & Tebaldi, Claudio, 2004. "Illiquid Assets and Optimal Portfolio Choice," University of California at Los Angeles, Anderson Graduate School of Management qt7q65t12x, Anderson Graduate School of Management, UCLA.
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    Cited by:

    1. Fabian Astic & Agnès Tourin, 2014. "Optimal bank management under capital and liquidity constraints," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 1-21.

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