The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
Stochastic Volatility for Lévy Processes
Open accessAbstract
Three processes reflecting persistence of volatility are initially formulated by evaluating three Lévy processes at a time change given by the integral of a mean‐reverting square root process. The model for the mean‐reverting time change is then generalized to include non‐Gaussian models that are solutions to Ornstein‐Uhlenbeck equations driven by one‐sided discontinuous Lévy processes permitting correlation with the stock. Positive stock price processes are obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating these processes. The characteristic functions for the log price can be used to yield option prices via the fast Fourier transform. In general mean‐corrected exponentiation performs better than employing the stochastic exponential. It is observed that the mean‐corrected exponential model is not a martingale in the filtration in which it is originally defined. This leads us to formulate and investigate the important property of martingale marginals where we seek martingales in altered filtrations consistent with the one‐dimensional marginal distributions of the level of the process at each future date.
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Cites
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Merton, R. C. (2019) · World Scientific Reference on Contingent Claims Analysis in Corporate Finance · doi:10.1142/9789814759588_0002 · Cited by 7,948
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Cited by
Lindgren, F., Rue, H., & Lindström, J. (2011) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2011.00777.x · Cited by 2,708
BOLLERSLEV, T., & TODOROV, V. (2011) · The Journal of Finance · doi:10.1111/j.1540-6261.2011.01695.x · Cited by 804
Time-changed Lévy processes and option pricing
Carr, P., & Wu, L. (2004) · Journal of Financial Economics · doi:10.1016/s0304-405x(03)00171-5 · Cited by 674
Self-citationEstimating quadratic variation using realized variance
Barndorff‐Nielsen, O. E., & Shephard, N. (2002) · Journal of Applied Econometrics · doi:10.1002/jae.691 · Cited by 616
Stochastic volatility with leverage: Fast and efficient likelihood inference
Omori, Y., Chib, S., Shephard, N., & Nakajima, J. (2007) · Journal of Econometrics · doi:10.1016/j.jeconom.2006.07.008 · Cited by 462
Metadata
- Authors
- Carr, P., Geman, H., Madan, D. B., & Yor, M.
- Venue
- Mathematical Finance
- Publisher
- Wiley
- Published
- 2003-05-29
- Volume
- 13
- Issue
- 3
- Pages
- 345-382
- ISSN
- 0960-1627 (ISSN-L)
- 1467-9965
- OpenAlex
- W3121574170
- Cited by
- 869
- References
- 28
- FWCI
- 51.34
- Type
- journal article
- Language
- en
- Open access
- green
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
