Jump-Diffusion Calibration using Differential Evolution

Ardia, David and Ospina, Juan and Giraldo, Giraldo (2010): Jump-Diffusion Calibration using Differential Evolution.

Abstract

The estimation of a jump-diffusion model via Differential Evolution is presented. Finding the maximum likelihood estimator for such processes is a tedious task due to the multimodality of the likelihood function. The performance of the Differential Evolution algorithm is compared to standard optimization techniques.

• Item Type: MPRA Paper
• Language: English
• Keywords: Jump-diffusion; maximum likelihood; optimization; Differential Evolution
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General

References

Ardia, D., Boudt, K., Carl, P., Mullen, K., Peterson, B., 2010. Differential Evolution (DEoptim) for non-convex portfolio optimization.

Ardia, D., Mullen, K., 2009. DEoptim: Differential Evolution Optimization in R. R package version 2.00-06. URL http://CRAN.R-project.org/package=DEoptim

Ball, C. A., Torous, W. N., 1983. A simplified jump process for common stock returns. The Journal of Financial and Quantitative Analysis 18 (1), 53–65.

Beckers, S., 1981. A note on estimating the parameters of the jump-diffusion model of stock returns. Journal of Financial and Quantitative Analysis 16, 127–140.

Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. The Journal of Political Economy 81 (3), 637–654.

Cont, R., Tankov, P., 2004. Financial Modelling with Jumps. Chapman & Hall / CRC Press, ISBN 1584884134.

Honore, P., 1998. Pitfalls in estimating jump-diffusion models.

Kiefer, N., 1978. Discrete parameter variation: Efficient estimation in diffusion process. Econometrica 46 (2), 427– 434.

Merton, R. C., 1973. Theory of rational option pricing. The Bell Journal of Economics and Management Science 4 (1), 141–183.

Mullen, K. M., Ardia, D., Gil, D. L., Windover, D., Cline, J., 2009. DEoptim: An R package for global optimization by Differential Evolution.

Ospina Arango, J. D., 2009. Estimacion de un modelo de difusion con saltos con distribucion de error generalizada asimitrica usando algoritmos evolutivos.

Price, K. V., Storn, R. M., Lampinen, J. A., 2006. Differential Evolution: A Practical Approach to Global Optimization. Springer-Verlag, Berlin, Germany, ISBN 3540209506.

R Development Core Team, 2009. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0.

URL http://www.R-project.org

Storn, R., Price, K., 1997. Differential Evolution – A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11 (4), 341–359.