2015/02/11 by Clément Ménassé, Peter Tankov, Ménassé, Clément +1
Economics, Econometrics and Finance · Social Sciences · #91G20 #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1502.03359
openalex publication_date 2015/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Financial markets based on Lévy processes are typically incomplete and option prices depend on risk attitudes of individual agents. In this context, the notion of utility indifference price has gained popularity in the academic circles. Although theoretically very appealing, this pricing method remains difficult to apply in practice, due to the high computational cost of solving the nonlinear partial integro-differential equation associated to the indifference price. In this work, we develop closed form approximations to exponential utility indifference prices in exponential Lévy models. To this end, we first establish a new non-asymptotic approximation of the indifference price which extends earlier results on small risk aversion asymptotics of this quantity. Next, we use this formula to derive a closed-form approximation of the indifference price by treating the Lévy model as a perturbation of the Black-Scholes model. This extends the methodology introduced in a recent paper for smooth linear functionals of Lévy processes (A. Černý, S. Denkl and J. Kallsen, arXiv:1309.7833) to nonlinear and non-smooth functionals. Our closed formula represents the indifference price as the linear combination of the Black-Scholes price and correction terms which depend on the variance, skewness and kurtosis of the underlying Lévy process, and the derivatives of the Black-Scholes price. As a by-product, we obtain a simple explicit formula for the spread between the buyer's and the seller's indifference price. This formula allows to quantify, in a model-independent fashion, how sensitive a given product is to jump risk in the limit of small jump size.