Approximation of jump diffusions in finance and economics
AbstractIn finance and economics the key dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, discrete time approximations are required. In this paper we give a survey of strong and weak numerical schemes for SDEs with jumps. Strong schemes provide pathwise approximations and therefore can be employed in scenario analysis, filtering or hedge simulation. Weak schemes are appropriate for problems such as derivative pricing or the evaluation of risk measures and expected utilities. Here only an approximation of the probability distribution of the jump-diffusion process is needed. As a framework for applications of these methods in finance and economics we use the benchmark approach. Strong approximation methods are illustrated by scenario simulations. Numerical results on the pricing of options on an index are presented using weak approximation methods. Copyright Springer Science+Business Media, LLC 2007
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Society for Computational Economics in its journal Computational Economics.
Volume (Year): 29 (2007)
Issue (Month): 3 (May)
Jump-diffusion processes; Discrete time approximation; Simulation; Strong convergence; Weak convergence; Benchmark approach; Growth Optimal portfolio; Primary 60H10; Secondary 65C05; G10; G13;
Other versions of this item:
- Nicola Bruti-Liberati & Eckhard Platen, 2006. "Approximation of Jump Diffusions in Finance and Economics," Research Paper Series 176, Quantitative Finance Research Centre, University of Technology, Sydney.
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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.:
- Nicola Bruti-Liberati & Eckhard Platen, 2005. "On the Strong Approximation of Jump-Diffusion Processes," Research Paper Series 157, Quantitative Finance Research Centre, University of Technology, Sydney.
- Guyon, Julien, 2006. "Euler scheme and tempered distributions," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 877-904, June.
- Nicola Bruti Liberati & Eckhard Platen, 2004. "On the Efficiency of Simplified Weak Taylor Schemes for Monte Carlo Simulation in Finance," Research Paper Series 114, Quantitative Finance Research Centre, University of Technology, Sydney.
- Merton, Robert C., 1976.
"Option pricing when underlying stock returns are discontinuous,"
Journal of Financial Economics,
Elsevier, vol. 3(1-2), pages 125-144.
- Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Mark Craddock & David Heath & Eckhard Platen, 1999. "Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing," Research Paper Series 27, Quantitative Finance Research Centre, University of Technology, Sydney.
- Kestutis Kubilius & Eckhard Platen, 2001. "Rate of Weak Convergence of the Euler Approximation for Diffusion Processes with Jumps," Research Paper Series 54, Quantitative Finance Research Centre, University of Technology, Sydney.
- Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
- Dennis Kristensen & Yongseok Shin, 2008.
"Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood,"
CREATES Research Papers
2008-58, School of Economics and Management, University of Aarhus.
- Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.