Valuation of volatility derivatives as an inverse problem
AbstractGround-breaking recent work by Carr and Lee extends well-known results for variance swaps to arbitrary functions of realized variance, provided a zero-correlation assumption is made. We give a detailed mathematical analysis of some of their computations and work out the cases of volatility swaps and calls on variance. The latter leads to an ill-posed problem that we solve using regularization techniques. The sum is divergent, that means we can do something Heaviside†
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Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Quantitative Finance.
Volume (Year): 5 (2005)
Issue (Month): 6 ()
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Web page: http://www.tandfonline.com/RQUF20
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- Claudio Albanese & Harry Lo & Aleksandar Mijatovic, 2009.
"Spectral methods for volatility derivatives,"
Taylor & Francis Journals, vol. 9(6), pages 663-692.
- Akihiko Takahashi & Yukihiro Tsuzuki & Akira Yamazaki, 2009. "Hedging European Derivatives with the Polynomial Variance Swap under Uncertain Volatility Environments," CARF F-Series CARF-F-161, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
- Gabriel G. Drimus, 2012. "Options on realized variance by transform methods: a non-affine stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 12(11), pages 1679-1694, November.
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