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Financial markets based on L\'evy processes are typically incomplete andoption prices depend on risk attitudes of individual agents. In this context,the notion of utility indifference price has gained popularity in the academiccircles. Although theoretically very appealing, this pricing method remainsdifficult to apply in practice, due to the high computational cost of solvingthe nonlinear partial integro-differential equation associated to theindifference price. In this work, we develop closed form approximations toexponential utility indifference prices in exponential L\'evy models. To thisend, we first establish a new non-asymptotic approximation of the indifferenceprice which extends earlier results on small risk aversion asymptotics of thisquantity. Next, we use this formula to derive a closed-form approximation ofthe indifference price by treating the L\'evy model as a perturbation of theBlack-Scholes model. This extends the methodology introduced in a recent paperfor smooth linear functionals of L\'evy processes (A. \v{C}ern\'y, S. Denkl andJ. Kallsen, arXiv:1309.7833) to nonlinear and non-smooth functionals. Ourclosed formula represents the indifference price as the linear combination ofthe Black-Scholes price and correction terms which depend on the variance,skewness and kurtosis of the underlying L\'evy process, and the derivatives ofthe Black-Scholes price. As a by-product, we obtain a simple explicit formulafor the spread between the buyer's and the seller's indifference price. Thisformula allows to quantify, in a model-independent fashion, how sensitive agiven product is to jump risk in the limit of small jump size.

Asymptotic indifference pricing in exponential L\'evy models