- Journal Article
Rights / licenseIn Copyright - Non-Commercial Use Permitted
Kramkov and Sîrbu (Ann. Appl. Probab., 16:2140–2194, 2006; Stoch. Proc. Appl., 117:1606–1620, 2017) have shown that first-order approximations of power utility-based prices and hedging strategies for a small number of claims can be computed by solving a mean-variance hedging problem under a specific equivalent martingale measure and relative to a suitable numeraire. For power utilities, we propose an alternative representation that avoids the change of numeraire. More specifically, we characterize the relevant quantities using semimartingale characteristics similarly as in Černý and Kallsen (Ann. Probab., 35:1479–1531, 2007) for mean-variance hedging. These results are illustrated by applying them to exponential Lévy processes and stochastic volatility models of Barndorff-Nielsen and Shephard type (J. R. Stat. Soc. B, 63:167–241, 2001). We find that asymptotic utility-based hedges are virtually independent of the investor’s risk aversion. Moreover, the price adjustments compared to the Black–Scholes model turn out to be almost linear in the investor’s risk aversion, and surprisingly small unless very high levels of risk aversion are considered. Show more
Journal / seriesMathematics and Financial Economics
Pages / Article No.
SubjectUtility-based pricing and hedging; Incomplete markets; Mean-variance hedging; Numeraire; Semimartingale characteristics
Organisational unit03899 - Muhle-Karbe, Johannes (ehemalig)
NotesIt was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
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