EUROPEAN OPTION PRICING WITH LIQUIDITY SHOCKS

Michael Ludkovski () and Qunying Shen ()
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Michael Ludkovski: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA
Qunying Shen: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2013, vol. 16, issue 07, 1-30

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 Hamilton–Jacobi–Bellman (HJB) equation satisfied by the indifference price, as well as its asymptotics when the probability of a liquidity shock is small. A comparative analysis between the model price and the classical Black–Scholes benchmark is given using the concepts of implied and adjusted time to maturity. 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.

Keywords: Liquidity shock; indifference price; exponential utility maximization (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (9)

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DOI: 10.1142/S021902491350043X

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