Partial Hedging In A Stochastic Volatility Environment
AbstractWe consider the problem of partial hedging of derivative risk in a stochastic volatility environment. It is related to state-dependent utility maximization problems in classical economics. We derive the dual problem from the Legendre transform of the associated Bellman equation and interpret the optimal strategy as the perfect hedging strategy for a modified claim. Under the assumption that volatility is fast mean-reverting and using a singular perturbation analysis, we derive approximate value functions and strategies that are easy to implement and study. The analysis identifies the usual mean historical volatility and the harmonically averaged long-run volatility as important statistics for such optimization problems without further specification of a stochastic volatility model. The approximation can be improved by specifying a model and can be calibrated for the leverage effect from the implied volatility skew. We study the effectiveness of these strategies using simulated stock paths. Copyright 2002 Blackwell Publishers.
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Bibliographic InfoArticle provided by Wiley Blackwell in its journal Mathematical Finance.
Volume (Year): 12 (2002)
Issue (Month): 4 ()
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627
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- Erhan Bayraktar & Xueying Hu & Virginia R. Young, 2010.
"Minimizing the Probability of Lifetime Ruin under Stochastic Volatility,"
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- Bayraktar, Erhan & Hu, Xueying & Young, Virginia R., 2011. "Minimizing the probability of lifetime ruin under stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 194-206, September.
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- Maxim Bichuch & Ronnie Sircar, 2014. "Optimal Investment with Transaction Costs and Stochastic Volatility," Papers 1401.0562, arXiv.org, revised Aug 2014.
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- Zhou, Qing & Wu, Weixing & Wang, Zengwu, 2008. "Cooperative hedging with a higher interest rate for borrowing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 609-616, April.
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