Valuing tradeability in exponential Lévy models

Ludovic Mathys; Ludovic Mathys

doi:10.3934/QFE.2020021

Quantitative Finance and Economics

2020, Volume 4, Issue 3: 459-488. doi: 10.3934/QFE.2020021

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Research article

Valuing tradeability in exponential Lévy models

Ludovic Mathys ^,

Department of Banking and Finance, University of Zurich, Zurich, Switzerland

Received: 15 May 2020 Accepted: 09 June 2020 Published: 29 June 2020
JEL Codes: C32, G12, G13

The present article provides a novel theoretical way to evaluate tradeability in markets of ordinary exponential Lévy type. We consider non-tradeability as a particular type of market illiquidity and investigate its impact on the price of the assets. Starting from an adaption of the continuous-time optional asset replacement problem initiated by McDonald and Siegel (1986), we derive tradeability premiums and subsequently characterize them in terms of free-boundary problems. This provides a simple way to compute non-tradeability values, e.g. by means of standard numerical techniques, and, in particular, to express the price of a non-tradeable asset as a percentage of the price of a tradeable equivalent. Our approach is illustrated via numerical examples where we discuss various properties of the tradeability premiums.
- tradeability,
- liquidity,
- exponential Lévy processes,
- real options,
- maturity-randomization,
- optimal stopping,
- free-boundary problems
Citation: Ludovic Mathys. Valuing tradeability in exponential Lévy models[J]. Quantitative Finance and Economics, 2020, 4(3): 459-488. doi: 10.3934/QFE.2020021

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Abstract

The present article provides a novel theoretical way to evaluate tradeability in markets of ordinary exponential Lévy type. We consider non-tradeability as a particular type of market illiquidity and investigate its impact on the price of the assets. Starting from an adaption of the continuous-time optional asset replacement problem initiated by McDonald and Siegel (1986), we derive tradeability premiums and subsequently characterize them in terms of free-boundary problems. This provides a simple way to compute non-tradeability values, e.g. by means of standard numerical techniques, and, in particular, to express the price of a non-tradeable asset as a percentage of the price of a tradeable equivalent. Our approach is illustrated via numerical examples where we discuss various properties of the tradeability premiums.

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