Location of Repository

Options on realized variance and convex orders

By P. Carr, Hélyette Geman, D.B. Madan and M. Yor


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

Topics: ems
Publisher: Taylor & Francis
Year: 2010
OAI identifier: oai:eprints.bbk.ac.uk.oai2:1947

Suggested articles



  1. (2009a), A construction of processes with one dimensional martingale marginals, based upon path-space OrnsteinUhlenbeck processes and the Brownian sheet, Prépublication Equipe dAnalyse et Probabilités, Université dEvry-Val dEssonne.
  2. (2009b), A construction of processes with one dimensional martingale marginals, associated with a Lévy process, via its Lévy sheet,Laboratoire dAnalyse et Probabilités, Université dEvry-Val dEssonne.
  3. (2008). A Brownian sheet martingale with the same marginals as the arithmetic average of geometric doi
  4. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options.Review of doi
  5. (2005). A note on su¢ cient conditions for no arbitrage,Finance doi
  6. (2001). Application of generalized hyperbolic Lévy motions to doi
  7. (2000). Evaluating probabilities for spectrally one-sided Lévy processes,Journal of Applied Probability, doi
  8. (1995). Hyperbolic distributions in doi
  9. (1999). Lévy Processes and in divisible distributions, doi
  10. (2008). New Measures for Performance Evaluation,Review of Financial Studies, doi
  11. (2001). Non-Gaussian OrnsteinUhlenbeck-based models and some of their uses in economics (with discussion),Journal of the Royal Statistical Society,
  12. (1995). Numerical Inversion of Laplace Transforms of Probability Distributions, doi
  13. (2008). On the qualitative e¤ect of volatility and duration on prices of Asian options,Finance doi
  14. (1999). Option valuation using the fast Fourier transform,Journal of
  15. (1978). Prices of state contingent claims implicit in options prices," doi
  16. (2009). Pricing and Hedging Basket Options to prespeci levels of Acceptability,forthcoming Quantitative Finance. doi
  17. (2009). Quelques résultats de croissance pour lordre convexe,Communication by letter.
  18. (2009). Sato processes and the valuation of structured products," Quantitative Finance, doi
  19. (2002). Stochastic Finance An Introduction doi
  20. (2003). Stochastic volatility for Lévy processes,Mathematical doi
  21. (2002). The structure of asset returns: An empirical investigation, doi
  22. (2002). The generalized hyperbolic model: Financial derivatives and risk measures,In Mathematical Finance-Bachelier Finance Congress doi
  23. (1973). The pricing of options and corporate liabilities. doi
  24. (2007). The range of traded options,Mathematical doi
  25. (1998). The variance gamma process and option pricing. doi
  26. (1973). Theory of rational option pricing. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.