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Valuing Tradeability in Exponential Lévy Models

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.