Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-25T00:04:47.126Z Has data issue: false hasContentIssue false
  • English
  • Français

SPATIAL DEPENDENCE AND AGGREGATION IN WEATHER RISK HEDGING: A LÉVY SUBORDINATED HIERARCHICAL ARCHIMEDEAN COPULAS (LSHAC) APPROACH

Published online by Cambridge University Press:  26 April 2018

Wenjun Zhu ,
Ken Seng Tan ,
Lysa Porth  and
Chou-Wen Wang
Wenjun Zhu*
Affiliation:
Nanyang Business School, Division of Banking & Finance, 50 Nanyang Avenue, 639798, Singapore
Ken Seng Tan
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, 200 University Ave. West, Waterloo, Ontario, Canada, E-Mail: kstan@uwaterloo.ca
Lysa Porth
Affiliation:
Warren Centre for Actuarial Studies and Research, University of Manitoba Asper School of Business, Winnipeg, Manitoba, Canada, E-Mail: lysa.porth@umanitoba.ca
Chou-Wen Wang
Affiliation:
Department of Finance, National Sun Yat-sen University, Kaohsiung, Taiwan, E-Mail: chouwenwang@mail.nsysu.edu.tw
*
E-Mail: wjzhu@ntu.edu.sg
Get access Rights & Permissions [Opens in a new window]

Abstract

Adverse weather-related risk is a main source of crop production loss and a big concern for agricultural insurers and reinsurers. In response, weather risk hedging may be valuable, however, due to basis risk it has been largely unsuccessful to date. This research proposes the Lévy subordinated hierarchical Archimedean copula model in modelling the spatial dependence of weather risk to reduce basis risk. The analysis shows that the Lévy subordinated hierarchical Archimedean copula model can improve the hedging performance through more accurate modelling of the dependence structure of weather risks and is more efficient in hedging extreme downside weather risk, compared to the benchmark copula models. Further, the results reveal that more effective hedging may be achieved as the spatial aggregation level increases. This research demonstrates that hedging weather risk is an important risk management method, and the approach outlined in this paper may be useful to insurers and reinsurers in the case of agriculture, as well as for other related risks in the property and casualty sector.

Keywords

Systemic weather riskhedging strategieshierarchical Archimedean copulasLévy subordinatorsagricultural insurancereinsuranceC13C15C16G17G22Q19Q14
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 2 , May 2018 , pp. 779 - 815
Copyright
Copyright © Astin Bulletin 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abdallah, A., Boucher, J.-P. and Cossette, H. (2015) Modeling dependence between loss triangles with hierarchical archimedean copulas. ASTIN Bulletin: A Journal of the IAA, 45 (3), 577–599.CrossRefGoogle Scholar
Acerbi, C. and Tasche, D. (2002) Expected shortfall: A natural coherent alternative to value at risk. Economic Notes, 31 (2), 379–388.CrossRefGoogle Scholar
Agriculture and Agri-Food Canada (AAFC) (2012) Evaluation of the Agriinsurance, Private Sector Risk Management Partnerships and Wildlife Compensation Programs. Technical Report AAFC No. 11985E, Agriculture and Agri-Food Canada, Office of Audit and Evaluation.Google Scholar
Alexandridis, A.K. and Zapranis, A.D. (2013) Weather Derivatives, Modeling and Pricing Weather-Related Risk. USA: Springer.CrossRefGoogle Scholar
Arbenz, P. and Canestraro, D. (2012) Estimating copulas for insurance from scarce observations, expert opinion and prior information: A bayesian approach. ASTIN Bulletin: A Journal of the IAA, 42 (1), 271–290.Google Scholar
Avanzi, B., Cassar, L.C. and Wong, B. (2011) Modelling dependence in insurance claims processes with lévy copulas. ASTIN Bulletin: A Journal of the IAA, 41 (2), 575–609.Google Scholar
Barth, A., Benth, F.E. and Potthoff, J. (2011) Hedging of spatial temperature risk with market-traded futures. Applied Mathematical Finance, 18 (2), 93–117.CrossRefGoogle Scholar
Benth, F.E. and Benth, J.Š. (2013) Modeling and Pricing in Financial Markets for Weather Derivatives. Singapore: World Scientific.Google Scholar
Bühlmann, H., Delbaen, F., Embrechts, P. and Shiryaev, A.N. (1996) No-arbitrage, change of measure and conditional Esscher transforms. CWI Quarterly, 9 (4), 291–317.Google Scholar
Campbell, S.D. and Diebold, F.X. (2005) Weather forecasting for weather derivatives. Journal of the American Statistical Association, 100 (469), 6–16.CrossRefGoogle Scholar
Carriquiry, M.A. and Osgood, D.E. (2012) Index insurance, probabilistic climate forecasts, and production. Journal of Risk and Insurance, 79 (1), 287–300.CrossRefGoogle Scholar
Chuliá, H., Guillén, M. and Uribe, J.M. (2016) Modeling longevity risk with generalized dynamic factor models and vine-copulae. ASTIN Bulletin: A Journal of the IAA, 46 (1), 165–190.CrossRefGoogle Scholar
Coble, K., Knight, T., Miller, M., Goodwin, B., Rejesus, R. and Boyles, R. (2013) Estimating structural change in u.s. crop insurance experience. Agricultural Finance Review, 73 (1), 74–87.CrossRefGoogle Scholar
Coble, K.H., Miller, M.F., Rejesus, R.M., Boyles, R., Knight, T.O. and Goodwin, B.K. (2011) Methodology Analysis for Weighting of Historical Experience. USDA Risk Management Agency.Google Scholar
Cummins, J.D., Lalonde, D. and Phillips, R.D. (2004) The basis risk of catastrophic-loss index securities. Journal of Financial Economics, 71, 77–111.CrossRefGoogle Scholar
Dischel, R.S. and Barrieu, P. (2002) Financial weather contracts and their application in risk management. In Climate Risk and the Weather Market: Financial Risk Management With Weather Hedges (ed. Dischel, R.S.), pp 25–42. London, UK: Risk Books.Google Scholar
Dong, W., Shah, H. and Wong, F. (1996) A rational approach to pricing of catastrophe. Journal of Risk and Uncertainty, 12 (2–3):201–218.CrossRefGoogle Scholar
Dupuis, D.J. (2012) Modeling waves of extremes temperature: The changing tails of four cities. Journal of the American Statistical Association, 107 (497), 24–39.CrossRefGoogle Scholar
Dupuis, D.J. (2014) A model for nighttime minimum temperatures. Journal of Climate, 27 (19), 7207–7229.CrossRefGoogle Scholar
Embrechts, P. and Hofert, M. (2013) Statistical inference for copulas in high dimensions: A simulation study. ASTIN Bulletin: A Journal of the IAA, 43 (2), 81–95.CrossRefGoogle Scholar
Embrechts, P., Lindskog, F. and McNeil (2003) Modelling dependence with copulas and applications to risk management. Handbook of Heavy Tailed Distributions in Finance, 8 (1), 329–284.CrossRefGoogle Scholar
Erhardt, R.J. (2015) Incorporating spatial dependence and climate change trends for measuring long-term temperature derivative risk. Variance, 9 (2), 213–226.Google Scholar
Erhardt, R.J. and Smith, R.L. (2014) Weather derivative risk measures for extreme events. North American Actuarial Journal, 18 (3), 379–393.CrossRefGoogle Scholar
Frittelli, M. (2000) The minimum entropy martingale measure and the valuation problem in incomplete markets. Mathematical Finance, 10 (1), 39–52.CrossRefGoogle Scholar
Gerber, H. and Shiu, S. (1994) Option pricing by Esscher transforms. Transaction of Society of Actuaries, 46, 99–140.Google Scholar
Golden, L.L., Wang, M. and Yang, C. (2007) Handling weather related risks through the financial markets: Considerations of credit risk, basis risk, and hedging. Journal of Risk and Insurance, 74 (2), 319–346.CrossRefGoogle Scholar
Goodwin, B.K. (2001) Problems with market insurance in agriculture. American Journal of Agriculture Economics, 83 (3), 643–649.CrossRefGoogle Scholar
Goodwin, B.K. and Hungerford, A. (2014) Copula-based models of systemic risk in U.S. agriculture: Implications for crop insurance and reinsurance contracts. American Journal of Agriculture Economics, 97 (3), 879–896.CrossRefGoogle Scholar
Härdle, W.K. and Osipenko, M. (2012) Spatial risk premium on weather derivatives and hedging weather exposure in electricity. The Energy Journal, 33 (2), 149–170.CrossRefGoogle Scholar
Hellmuth, M.E., Osgood, D.E., Hess, U., Moorhead, A. and Bhojwani, H. (2009) Index insurance and climate risk: Prospects for development and disaster management. Technical Report No. 2, Climate and Society, International Research Institute for Climate and Society, New York, USA.Google Scholar
Hering, C., Hofert, M., Mai, J.-F. and Scherer, M. (2010) Constructing hierarchical archimedean copulas with lévy subordinators. Journal of Multivariate Analysis, 101 (6), 1428–1433.CrossRefGoogle Scholar
Hong, H., Li, F.W. and Xu, J. (2016) Climate Risks and Market Efficiency. Columbia University, Working Paper.CrossRefGoogle Scholar
Hubalek, J. and Neilsen, B. (2006) On the Esscher transform and entropy for exponential Lévy models. Quantitative Finance, 6 (2), 125–145.CrossRefGoogle Scholar
Hürlimann, W. (2014) On some properties of two vector-valued VaR and CTE multivariate risk measures for Archimedean copulas. ASTIN Bulletin: A Journal of the IAA, 44 (3), 613–633.CrossRefGoogle Scholar
IPCC (2007) Fourth Assessment Report. Technical report, Intergovernmental Panel on Climate Change.Google Scholar
Joe, H. (1997) Multivariate Models and Dependence Concepts. Boca Raton: Chapman & Hall.Google Scholar
Li, J.S.-H. and Hardy, M.R. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15 (2), 177–200.CrossRefGoogle Scholar
Li, J.S.-H., Hardy, M.R. and Tan, K.S. (2010) On pricing and hedging the no-negative-equity guarantee in equity release mechanisms. Journal of Risk and Insurance, 77 (2), 499–522.Google Scholar
Lobell, D.B. and Burke, M.B. (2008) Why are agricultural impacts of climate change so uncertain? The importance of temperature relative to precipitation. Environmental Research Letters, 3 (1), 1–8.CrossRefGoogle Scholar
Mahul, O. and Stutley, C.J. (2010) Government Support to Agricultural Insurance: Challenges and Options for Developing Countries. Washington D.C.: World Bank Publications.CrossRefGoogle Scholar
Mai, J.-F. and Scherer, M. (2012) H-extendible copulas. Journal of Multivariate Analysis, 110, 151–160.CrossRefGoogle Scholar
McNeil, A.J. (2008) Sampling nested archimedean copulas. Journal of Statistical Computation and Simulation, 78 (6), 567–581.CrossRefGoogle Scholar
McNeil, A.J., Frey, R. and Embrechts, P. (2010) Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton, NJ: Princeton University Press.Google Scholar
Miranda, M. and Glauber, J. (1997) Systemic risk, reinsurance and the failure of crop insurance market. American Journal of Agriculture Economics, 79 (1), 206–215.CrossRefGoogle Scholar
Nelson, D.B. (1991) Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59 (2), 347–370.CrossRefGoogle Scholar
Odening, M. and Shen, Z. (2012) Challenges of insuring weather risk in agriculture. Agricultural Finance Review, 74 (2), 188–199.CrossRefGoogle Scholar
Okhrin, O., Odening, M. and Xu, W. (2013a) Systemic weather risk and crop insurance: The case of china. Journal of Risk and Insurance, 80 (2), 351–372.CrossRefGoogle Scholar
Okhrin, O., Okhrin, Y. and Schmid, W. (2013b) On the structure and estimation of hierarchical archimedean copulas. Journal of Econometrics, 173 (1), 189–204.CrossRefGoogle Scholar
Parodi, P. (2014) Pricing in General Insurance. Boca Raton: CRC Press.CrossRefGoogle Scholar
Pérez-González, F. and Yun, H. (2013) Risk management and firm value: Evidence from weather derivatives. Journal of Finance, LXVIII (5), 2143–2176.CrossRefGoogle Scholar
Porth, L., Pai, J. and Boyd, M. (2015) A portfolio optimization approach using combinatorics with a genetic algorithm for developing a reinsurance model. Journal of Risk and Insurance, 82 (3), 687–713.CrossRefGoogle Scholar
Porth, L., Tan, K.S. and Weng, C. (2013) Optimal reinsurance analysis from a crop insurer's perspective. Agriculture Finance Review, 73 (2), 310–328.CrossRefGoogle Scholar
Porth, L., Zhu, W. and Tan, K.S. (2014b) A credibility-based Erlang mixture model for pricing crop reinsurance. Agricultural Finance Review, 74 (2), 162–187.CrossRefGoogle Scholar
Priest, G.L. (1996) The government, the market, and the problem of catastrophic loss. Journal of Risk and Uncertainty, 12 (2–3), 219–237.CrossRefGoogle Scholar
Šaltytė Benth, J. and Šaltytė, L. (2011) Spatial–temporal model for wind speed in lithuania. Journal of Applied Statistics, 38 (6), 1151–1168.CrossRefGoogle Scholar
Savu, C. and Trede, M. (2010) Hierarchies of archimedean copulas. Quantitative Finance, 10 (3), 295–304.CrossRefGoogle Scholar
Schneider, K. and Roth, M. (2013) Growing premium. Insider Quarterly. Available at: http://www.insiderquarterly.com/growing-premiumGoogle Scholar
Shi, P. (2014) A copula regression for modeling multivariate loss triangles and quantifying reserving variability. ASTIN Bulletin: A Journal of the IAA, 4 (1), 85–102.CrossRefGoogle Scholar
Shi, P. and Frees, E.W. (2011) Dependent loss reserving using copulas. ASTIN Bulletin: A Journal of the IAA, 41 (2), 449–486.Google Scholar
Siu, T., Tong, H. and Yang, H. (2004) On pricing derivatives under garch models: A dynamic gerber-shiu approach. North American Actuarial Journal, 8, 17–31.CrossRefGoogle Scholar
Székely, G.J. and Rizzo, M.L. (2005) Hierarchical clustering via joint between-within distance: Extending Ward's minimum variance method. Journal of Classification, 22 (2), 151–183.CrossRefGoogle Scholar
Tankov, P. (2004) Financial Modelling with Jump Processes. Boca Raton: CRC Press.Google Scholar
Turvey, C.G. (2005) The pricing of degree-day weather options. Agricultural Finance Review, 65 (1), 59–85.CrossRefGoogle Scholar
Turvey, C.G., Weersink, A. and Chiang, S.H.C. (2006) Pricing weather insurance with random strike price: The ontario ice-wine harvest. American Journal of Agriculture Economics, 88 (1), 696–709.CrossRefGoogle Scholar
USDA (2014) World Agricultural Supply and Demand Estimates Report (WASDE). Technical report, Office of the chief economist (OCE), United States Department of Agriculture.Google Scholar
Ward, J.H. (1963) Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58 (301), 236–244.CrossRefGoogle Scholar
Whelan, N. (2004) Sampling from archimedean copulas. Quantitative Finance, 4 (3), 339–352.CrossRefGoogle Scholar
Woodard, J.D. and Garcia, P. (2008a) Basis risk and weather hedging effectiveness. Agricultural Finance Review, 68 (1), 99–117.CrossRefGoogle Scholar
Woodard, J.D. and Garcia, P. (2008b) Weather derivatives, spatial aggregation, and systemic risk: Implications for reinsurance hedging. Journal of Agricultural and Resource Economics, 33 (1), 34–51.Google Scholar
Woodard, J.D., Schnitkey, G.D., Sherrick, B.J., Lozano-Gracia, N. and Anselin, L. (2012) A spatial econometric analysis of loss experience in the U.S. crop insurance program. Journal of Risk and Insurance, 79 (1), 261–286.CrossRefGoogle Scholar
Yang, J., Chen, Z., Wang, F. and Wang, R. (2015) Composite bernstein copulas. ASTIN Bulletin: A Journal of the IAA, 45 (2), 445–475.CrossRefGoogle Scholar
Yang, M. (2011) Volatility feedback and risk premium in Garch models with generalized hyperbolic distributions. Studies in Nonlinear Dynamics & Econometrics, 15 (3), 1558–3708.Google Scholar
Zhang, W., Zhao, D. and Wang, X. (2013) Agglomerative clustering via maximum incremental path integral. Pattern Recognition, 46 (11), 3056–3065.CrossRefGoogle Scholar
Zhu, W., Wang, C.-W. and Tan, K.S. (2016) Structure and estimation of Lévy subordinated hierarchical archimedean copulas (LSHAC): Theory and empirical tests. Journal of Banking & Finance, 69, 20–36.CrossRefGoogle Scholar
Zhu, W., Wang, C.-W. and Tan, K.S. (2017) Modeling multi-population longevity risk with mortality dependence: A Lévy subordinated hierarchical archimedean copulas (LSHAC) approach. Journal of Risk and Insurance, 84 (1), 477–493.CrossRefGoogle Scholar