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Options on realized variance and convex orders

Carr, P. and Geman, Hélyette and Madan, D.B. and Yor, M. (2010) Options on realized variance and convex orders. Quantitative Finance 11 (11), pp. 1685-1694. ISSN 1469-7688.

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Realized variance option and options on quadratic variation normalized to unit expectation are analysed for the property of monotonicity in maturity for call options at a fixed strike. When this condition holds the risk-neutral densities are said to be increasing in the convex order. For Leacutevy processes, such prices decrease with maturity. A time series analysis of squared log returns on the S&P 500 index also reveals such a decrease. If options are priced to a slightly increasing level of acceptability, then the resulting risk-neutral densities can be increasing in the convex order. Calibrated stochastic volatility models yield possibilities in both directions. Finally, we consider modeling strategies guaranteeing an increase in convex order for the normalized quadratic variation. These strategies model instantaneous variance as a normalized exponential of a Leacutevy process. Simulation studies suggest that other transformations may also deliver an increase in the convex order.

Item Type: Article
Additional Information: Published online first
Keyword(s) / Subject(s): Equity options, Levy process, mathematical finance, stochastic volatility, stochastic processes
School or Research Centre: Birkbeck Schools and Research Centres > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
Depositing User: Administrator
Date Deposited: 02 Dec 2010 08:34
Last Modified: 17 Apr 2013 12:33

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