Continuous Time Regime Switching Models and Applications in Estimating Processes with Stochastic Volatility and Jumps
A regime switching model in continuous time is introduced where a variety of jumps are allowed in addition to the diffusive component. The characteristic function of the process is derived in closed form, and is subsequently employed to create the likelihood function. In addition, standard results of the option pricing literature can be employed in order to compute derivative prices. To this end, the relationship between the physical and the risk adjusted probability measure is explored. The generic relationship between Markov chains and [jump] diffusions is also investigated, and it is shown that virtually any stochastic volatility model model can be approximated arbitrarily well by a carefully chosen continuous time Markov chain. Therefore, the approach presented here can be utilized in order to estimate, filter and carry out option pricing for such continuous state-space models, without the need for simulation based approximations. An empirical example illustrates these contributions of the paper, estimating a stochastic volatility jump diffusion model.
|Date of creation:||Nov 2002|
|Date of revision:|
|Contact details of provider:|| Postal: London E1 4NS|
Phone: +44 (0) 20 7882 5096
Fax: +44 (0) 20 8983 3580
Web page: http://www.econ.qmul.ac.uk
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
- Carl Chiarella & Sara Pasquali & Wolfgang Runggaldier, 2001. "On Filtering in Markovian Term Structure Models (An Approximation Approach)," Research Paper Series 65, Quantitative Finance Research Centre, University of Technology, Sydney.
- Jarrow, Robert A & Lando, David & Turnbull, Stuart M, 1997. "A Markov Model for the Term Structure of Credit Risk Spreads," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 481-523.
- Andrew W. Lo & Jiang Wang, 1994.
"Implementing Option Pricing Models When Asset Returns Are Predictable,"
NBER Working Papers
4720, National Bureau of Economic Research, Inc.
- Lo, Andrew W & Wang, Jiang, 1995. " Implementing Option Pricing Models When Asset Returns Are Predictable," Journal of Finance, American Finance Association, vol. 50(1), pages 87-129, March.
- Lo, Andrew W. (Andrew Wen-Chuan) & Wang, Jiang, 1959-, 1993. "Implementing option pricing models when asset returns are predictable," Working papers 3593-93., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
- Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
- Kooperberg, Charles & Stone, Charles J., 1991. "A study of logspline density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 12(3), pages 327-347, November.
- Naik, Vasanttilak, 1993. " Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-84, December.
- David S. Bates, . "Testing Option Pricing Models," Rodney L. White Center for Financial Research Working Papers 14-95, Wharton School Rodney L. White Center for Financial Research.
- Daniel B. Nelson & Dean P. Foster, 1994.
"Asypmtotic Filtering Theory for Univariate Arch Models,"
NBER Technical Working Papers
0129, National Bureau of Economic Research, Inc.
- Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
- David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
- Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
When requesting a correction, please mention this item's handle: RePEc:qmw:qmwecw:wp464. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Nick Vriend)
If references are entirely missing, you can add them using this form.