Valuing Tradeability in Exponential L\'evy Models

TL;DR

This paper introduces a new theoretical framework to quantify tradeability in markets modeled by exponential Lévy processes, linking market illiquidity to asset pricing through free-boundary problems.

Contribution

It develops a novel method to evaluate tradeability premiums in exponential Lévy models using free-boundary problems, enabling practical computation of non-tradeability values.

Findings

Tradeability premiums can be expressed via free-boundary problems.

Non-tradeability values are computable using standard numerical methods.

The approach allows expressing non-tradeable asset prices as a percentage of tradeable equivalents.

Abstract

The present article provides a novel theoretical way to evaluate tradeability in markets of ordinary exponential L\'evy 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.