A Levy Regime-Switching Temperature Dynamics Model for Weather Derivatives

Asante Gyamerah, Samuel and Ngare, Philip and Ikpe, Dennis (2018): A Levy Regime-Switching Temperature Dynamics Model for Weather Derivatives. Published in: International Journal of Stochastic Analysis , Vol. 2018, No. 8534131 (10 June 2018): pp. 1-16.

Abstract

Weather is a key production factor in agricultural crop production and at the same time the most significant and least controllable source of peril in agriculture. These effects of weather on agricultural crop production have triggered a widespread support for weather derivatives as a means of mitigating the risk associated with climate change on agriculture. However, these products are faced with basis risk as a result of poor design and modelling of the underlying weather variable (temperature). In order to circumvent these problems, a novel time-varying mean-reversion L´evy regime-switching model is used to model the dynamics of the deseasonalized temperature dynamics. Using plots and test statistics, it is observed that the residuals of the deseasonalized temperature data are not normally distributed. To model the nonnormality in the residuals, we propose using the hyperbolic distribution to capture the semiheavy tails and skewness in the empirical distributions of the residuals for the shifted regime. The proposed regime-switching model has a mean-reverting heteroskedastic process in the base regime and a Levy process in the shifted regime. By using the Expectation-Maximization algorithm, the parameters of the proposed model are estimated. The proposed model is flexible as it modelled the deseasonalized temperature data accurately.

• Item Type: MPRA Paper
• Language: English
• Keywords: Levy Process, Weather Derivative, Temperature, Regime-Switching
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C55 - Large Data Sets: Modeling and Analysis; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q5 - Environmental Economics; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q5 - Environmental Economics > Q54 - Climate ; Natural Disasters and Their Management ; Global Warming

References

Adger, W. N., Huq, S., Brown, K., Conway, D., and Hulme, M. (2003). Adaptation to climate change in the developing world. Progress in development studies, 3(3),179-195.

Alaton, P., Djehiche, B., and Stillberger, D. (2002). On modelling and pricing weather derivatives. Applied mathematical finance, 9(1),1-20.

Barndorff-Nielsen, O. (1977). Exponentially decreasing distributions for the logarithm of particle size. Proc. R. Soc. Lond. A,353(1674),401-419.

Barndorff-Nielsen, O. E. (1997). Processes of normal inverse gaussian type. Finance and stochastics, 2(1),41-68.

Benth, F. E. and Benth, J. s. (2007). The volatility of temperature and pricing of weather derivatives. Quantitative Finance, 7(5),553-561.

Benth, F. E. and Saltyte-Benth, J. (2005). Stochastic modelling of temperature variations with a view towards weather derivatives. Applied Mathematical Finance, 12(1),53-85.

Brockett, P. L., Goldens, L. L., Wen, M.-M., and Yang, C. C. (2009). Pricing weather derivatives using the indifference pricing approach. North American Actuarial Journal, 13(3),303-315.

Brody, D. C., Syroka, J., Zervos, M., et al. (2002). Dynamical pricing of weather derivatives. Quantitative Finance, 2(3),189-198.

Bryan, E., Deressa, T. T., Gbetibouo, G. A., and Ringler, C. (2009). Adaptation to climate change in ethiopia and south africa: options and constraints. environmental science & policy, 12(4), 413-426.

Chevallier, J. and Goutte, S. (2015). Detecting jumps and regime switches in international stock markets returns. Applied Economics Letters, 22(13),1011-1019.

Chevallier, J. and Goutte, S. (2017a). Cross-country performance of Lévy regime-switching models for stock markets. Applied Economics, 49(2),111-137.

Chevallier, J. and Goutte, S. (2017b).Estimation of Lévy-driven Ornstein–Uhlenbeck processes: application to modeling of CO2 and fuel-switching. Annals of Operations Research, 255(1-2),169-197.

Christiaensen, L. J. (2007). Down to earth: agriculture and poverty reduction in Africa. World Bank Publications.

Cui, K. (2014). Weather Derivatives: Modelling, Pricing and Applications. PhD thesis, University of Calgary.

Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the royal statistical society. Series B (methodological), pages 1-38.

Dischel, B. (1999). Black-scholes won't do. Risk, 10, 8-9.

Dornier, F. and Queruel, M. (2000). Caution to the wind. Energy & power risk management, 13(8),30-32.

Elias, R., Wahab, M., and Fang, L. (2014). A comparison of regime-switching temperature modeling approaches for applications in weather derivatives. European Journal of Operational Research, 232(3),549-560.

Evarest, E., Berntsson, F., Singull, M., and Charles, W. (2016). Regime switching models on temperature dynamics.

Gordon, R. and Bootsma, A. (1993). Analyses of growing degree-days for agriculture in atlantic canada. Climate Research, pages 169-176.

Gyamerah, S. and Ngare, P. (2018). Regime-switching model on hourly electricity spot price dynamics. Journal of Mathematical Finance, 8(1),102-110.

Hamilton, J. D. (1988). Rational-expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates. Journal of Economic Dynamics and Control, 12(2-3),385-423.

Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica: Journal of the Econometric Society, pages 357-384.

Hatfield, J. L. and Prueger, J. H. (2015). Temperature extremes: effect on plant growth and development. Weather and climate extremes, 10,4-10.

Kim, C.-J. (1994). Dynamic linear models with markov-switching. Journal of Econometrics, 60(1-2),1-22.

Madan, D. B., Carr, P. P., and Chang, E. C. (1998). The variance gamma process and option pricing. Review of Finance, 2(1),79-105.

McIntyre, R. and Doherty, S. (1999). Weather risk-an example from the uk. Energy and Power Risk Management, June.

Nicola, F. d., Hill, R. V., Carter, M., Choularton, R., Hansen, J., and Osgood, D. (2011). Index insurance for managing climate-related agricultural risk: toward a strategic research agenda.

Ochieng, J., Kirimi, L., and Mathenge, M. (2016). Effects of climate variability and change on agricultural production: The case of small scale farmers in kenya. NJAS-Wageningen Journal of Life Sciences, 77,71-78.

Schaller, H. and Norden, S. V. (1997). Regime switching in stock market returns. Applied Financial Economics, 7(2),177-191.

Weron, R. (2009). Heavy-tails and regime-switching in electricity prices. Mathematical Methods of Operations Research, 69(3),457-473.

Zapranis, A. and Alexandridis, A. (2009). Weather derivatives pricing: Modeling the seasonal residual variance of an ornstein-uhlenbeck temperature process with neural networks. Neurocomputing, 73(1),37-48.