On time scaling of semivariance in a jump-diffusion process
The aim of this paper is to examine the time scaling of the semivariance when returns are modeled by various types of jump-diffusion processes, including stochastic volatility models with jumps in returns and in volatility. In particular, we derive an exact formula for the semivariance when the volatility is kept constant, explaining how it should be scaled when considering a lower frequency. We also provide and justify the use of a generalization of the Ball-Torous approximation of a jump-diffusion process, this new model appearing to deliver a more accurate estimation of the downside risk. We use Markov Chain Monte Carlo (MCMC) methods to fit our stochastic volatility model. For the tests, we apply our methodology to a highly skewed set of returns based on the Barclays US High Yield Index, where we compare different time scalings for the semivariance. Our work shows that the square root of the time horizon seems to be a poor approximation in the context of semivariance and that our methodology based on jump-diffusion processes gives much better results.
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.:
- Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-26, March.
- Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
- 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.
- Katharine M. Mullen & David Ardia & David L. Gil & Donald Windover & James Cline, .
"DEoptim: An R Package for Global Optimization by Differential Evolution,"
Journal of Statistical Software,
American Statistical Association, vol. 40(i06).
- Mullen, Katharine M. & Ardia, David & Gil, David L. & Windover, Donald & Cline, James, 2009. "DEoptim: An R Package for Global Optimization by Differential Evolution," MPRA Paper 21743, University Library of Munich, Germany, revised 26 Dec 2010.
- Ardia, David & Ospina, Juan & Giraldo, Giraldo, 2010. "Jump-Diffusion Calibration using Differential Evolution," MPRA Paper 26184, University Library of Munich, Germany, revised 25 Oct 2010.
- Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997.
" Empirical Performance of Alternative Option Pricing Models,"
Journal of Finance,
American Finance Association, vol. 52(5), pages 2003-49, December.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
- Jean-Pierre Zigrand & Jon Danielsson, 2003.
"On time-scaling of risk and the square–root–of–time rule,"
FMG Discussion Papers
dp439, Financial Markets Group.
- Danielsson, Jon & Zigrand, Jean-Pierre, 2006. "On time-scaling of risk and the square-root-of-time rule," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2701-2713, October.
- Jon Danielsson & Jean-Pierre Zigrand, 2003. "On time-scaling of risk and the square–root–of–time rule," LSE Research Online Documents on Economics 24827, London School of Economics and Political Science, LSE Library.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- 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.
- Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
- Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
- Ball, Clifford A & Torous, Walter N, 1985. " On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-73, March.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1311.1122. 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: (arXiv administrators)
If references are entirely missing, you can add them using this form.