×

An extension of spatial dependence models for estimating short-term temperature portfolio risk. (English) Zbl 1416.91174

Summary: Temperature risk is any adverse financial outcome caused by temperature outcomes. The Chicago Mercantile Exchange lists a series of financial products that link payments to temperature outcomes, and these products can help buyers manage temperature risk. Financial institutions can also hold a portfolio of these products as counterparty to the buyers facing temperature risk. Here we take an actuarial perspective to measuring the risk by modeling the daily temperatures directly. These models are then used to simulate distributions of future temperature outcomes. The model for daily temperature is a spatial ARMA-EGARCH statistical model that incorporates dependence in both time and space, in addition to modeling the volatility. Simulations from this model are used to build up distributions of temperature outcomes, and we demonstrate how actuarial risk measures of the portfolio can then be estimated from these distributions.

MSC:

91B30 Risk theory, insurance (MSC2010)
91-04 Software, source code, etc. for problems pertaining to game theory, economics, and finance
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Benth, F. E.; Šaltytė Benth, J., Modeling and Pricing in Financial Markets for Weather Derivatives, (2013), World Scientific, Singapore · Zbl 1303.91004
[2] Bollerslev, T.; Wooldridge, J. M., Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances, Econometric Reviews, 11, 2, 143-172, (1992) · Zbl 0850.62884
[3] Brockett, P. L.; Wang, M.; Yang, C., Weather derivatives and weather risk management, Risk Management and Insurance Review, 8, 1, 127-140, (2005)
[4] Brockett, P. L.; Wang, M.; Yang, C.; Zou, H., Portfolio effects and valuation of weather derivatives, Financial Review, 41, 1, 55-76, (2006)
[5] Campbell, S. D.; Diebold, F. X., Weather forecasting for weather derivatives, Journal of the American Statistical Association, 100, 469, 6-16, (2005) · Zbl 1117.62305
[6] Dischel, R., Climate Risk and the Weather Market: Financial Risk Management Weather Hedges, (2002), Risk Publications, London
[7] Dupuis, D. J., Forecasting temperature to price CME temperature derivatives, International Journal of Forecasting, 27, 2, 602-618, (2011)
[8] Dupuis, D. J., Modeling waves of extreme temperature: the changing tails of four cities, Journal of the American Statistical Association, 107, 497, 24-39, (2012) · Zbl 1261.62104
[9] Dupuis, D. J., A model for night-time minimum temperatures, Journal of Climate, 27, 19, 7207-7229, (2014)
[10] Dutton, J. A., Opportunities and priorities in a new era for weather and climate services, Bulletin of the American Meteorological Society, 83, 9, 1303-1311, (2002)
[11] Erhardt, R., Mid-twenty-first-century projected trends in north American heating and cooling degree days, Environmetrics, 26, 2, 133-144, (2014)
[12] Erhardt, R.; Smith, R., Weather derivative risk measures for extreme events, North American Actuarial Journal, 18, 3, 379-393, (2014)
[13] Erhardt, R., Incorporating spatial dependence and climate change trends for measuring long-term temperature derivative risk, Variance, 9, 2, 213-226, (2016)
[14] Fisher, T. J.; Gallagher, C. M., New weighted portmanteau statistics for time series goodness of fit testing, Journal of the American Statistical Association, 107, 498, 777-787, (2012) · Zbl 1261.62079
[15] Franses, P. H.; Neele, J.; van Dijk, D., Modeling asymmetric volatility in weekly Dutch temperature data, Environmental Modelling & Software, 16, 2, 131-137, (2001)
[16] Geman, H., Insurance and Weather Derivatives: From Exotic Options to Exotic Underlyings, (1999), Risk Publications, London
[17] 2013Rugarch: univariate GARCH modelsR package version 1.2-7ViennaR Foundation
[18] Jewson, S., Introduction to weather derivative pricing, Journal of Alternative Investments, 7, 2, 57-64, (2004)
[19] Jewson, S.; Brix, A.; Ziehmann, C., Weather Derivative Valuation: The Meteorological, Statistical, Financial and Mathematical Foundations, (2005), Cambridge University Press, Cambridge
[20] Kass, R.; Goovaerts, M.; Dhaene, J.; Denuit, M., Modern Actuarial Risk Theory, (2008), Springer, 2nd ed. New York
[21] Kunreuther, H.; Michel-Kerjan, E., At War with the Weather: Managing Large-Scale Risks in a New Era of Catastrophes, (2009), MIT Press, Cambridge, MA
[22] Li, W. K.; Mak, T. K., On the squared residual autocorrelations in nonlinear time series with conditional heteroskedasticity, Journal of Time Series Analysis, 15, 6, 627-636, (1994) · Zbl 0807.62070
[23] 1991Conditional heteroskedasticity in asset returns: A new approachEconometrica: Journal of the Econometric Society59347370
[24] Newey, W. K.; McFadden, D., Large sample estimation and hypothesis testing, Handbook of Econometrics, 4, 2111-2245, (1994)
[25] Pascual, L.; Romo, J.; Ruiz, E., Bootstrap prediction for returns and volatilities in garch models, Computational Statistics and Data Analysis, 50, 9, 2293-2312, (2006) · Zbl 1445.62314
[26] Richards, T.; Manfredo, M.; Sanders, D., Pricing weather derivatives, American Journal of Agricultural Economics, 86, 4, 1005-1017, (2004)
[27] Ritter, M.; Musshoff, O.; Odening, M., Minimizing geographical basis risk of weather derivatives using a multi-site rainfall model, Computational Economics, 44, 1, 67-86, (2014)
[28] Šaltytė Benth, J.; Benth, F. E., A critical view on temperature modelling for application in weather derivatives markets, Energy Economics, 34, 2, 592-602, (2012)
[29] Šaltytė Benth, J.; Benth, F.; Jalinskas, P., A spatial-temporal model for temperature with seasonal variance, Journal of Applied Statistics, 34, 7, 823-841, (2007)
[30] Šaltytė Benth, J.; Saltyte, L., Spatialtemporal model for wind speed in Lithuania, Journal of Applied Statistics, 38, 6, 1151-1168, (2011)
[31] Taylor, J. W.; Buizza, R., Density forecasting for weather derivative pricing, International Journal of Forecasting, 22, 1, 29-42, (2006)
[32] 2007Spatial aggregation and weather risk managementAmerican Agricultural Economics Association Annual Meeting, Portland, OR, July
[33] Zeng, L., Weather derivatives and weather insurance: concept, application, and analysis, Bulletin of the American Meteorological Society, 81, 9, 2075-2082, (2000)
[34] Zivot, E.; Wang, J., Modeling Financial Time Series with S-Plus, 191, (2007), Springer Science and Business Media, New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.