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Asymptotic power utility-based pricing and hedging

Content Provider	Springer Nature Link
Author	Kallsen, Jan Muhle Karbe, Johannes Vierthauer, Richard
Copyright Year	2013
Abstract	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.
Starting Page	1
Ending Page	28
Page Count	28
File Format	PDF
ISSN	18629679
Journal	Mathematics and Financial Economics
Volume Number	8
Issue Number	1
e-ISSN	18629660
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-01-20
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Utility-based pricing and hedging Incomplete markets Mean-variance hedging Numeraire Semimartingale characteristics Quantitative Finance Finance/Investment/Banking Financial Economics Game Theory/Mathematical Methods Applications of Mathematics Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Finance Statistics and Probability Statistics, Probability and Uncertainty

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