Pricing weather derivatives using the indifference pricing approach. (English) Zbl 1483.91229

Summary: This paper adopts an incomplete market pricing model – the indifference pricing approach – to analyze valuation of weather derivatives and the viability of the weather derivatives market in a hedging context. It incorporates price risk, weather/quantity risk, and other risks in the financial market. In a mean-variance framework, the relationship between the actuarial price and the indifference price of weather derivatives is analyzed, and conditions are obtained concerning when the actuarial price does not provide an appropriate valuation for weather derivatives. Conditions for the viability of the weather derivatives market are examined. This paper also analyzes the effects of partial hedging, natural hedges, basis risk, quantity risk, and price risk on investors’ indifference prices by examining the distributional impacts of the stochastic variables involved.


91G20 Derivative securities (option pricing, hedging, etc.)
Full Text: DOI


[1] Barrieu, P. and El Karoui, N. 2002. Optimal Design of Derivatives in Illiquid Assets. Quantitative Finance, 2(3): 181-188. · Zbl 1405.91584
[2] Bessembinder, H. and Lemmon, M. 2002. Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets. Journal of Finance, 57(3): 1347-82.
[3] Black, F. and SCholes, M. 1973. The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81: 637-55. · Zbl 1092.91524
[4] Bouleau, N. and Lamberton, D. 1989. Residual Risks and Hedging Strategies in Markovian Markets. Stochastic Processes and Their Applications, 33: 131-50. · Zbl 0743.60069
[5] Brockett, P., Wang, M. and Yang, C. 2005. Weather Derivatives and Weather Risk Management. Risk Management and Insurance Review, 8(1): 127-40.
[6] Brockett, P., Wang, M., Yang, C. and Zou, H. 2006. Portfolio Effects and Valuation of Weather Derivatives. Financial Review, 41: 55-76.
[7] Cao, M. and Wei, J. 2003. Weather Derivatives Valuation and Market Price of Weather Risk. Journal of Futures Markets, 24: 1065-90.
[8] Craft, E. 1998. The Value of Weather Information Services for Nineteenth-Century Great Lakes Shipping. American Economic Review, 88(5): 1059-76.
[9] Cvitanic, J. 1998. Minimizing Expected Loss of Hedging in Incomplete and Constrained Markets, Columbia University. Preprint
[10] Davis, M. 1998. “Option Pricing in Incomplete Markets”. In Mathematics of Derivative Securities, New York: Cambridge University Press. · Zbl 0914.90017
[11] Davis, M. 2001. Pricing Weather Derivatives by Marginal Value. Quantitative Finance, 1: 1-4.
[12] Davis, M., Panas, V. and Zariphoupoulou, T. 1993. European Option Pricing with Transaction Costs. SIAM Journal on Control and Optimization, 31: 470-93. · Zbl 0779.90011
[13] Dischel, B. 1998. Weather Sensitivity, Weather Derivatives and a Pricing Model. Focus,
[14] Doherty, N. and Richter, A. 2002. Moral Hazard, Basis Risk and Gap Insurance. Journal of Risk and Insurance, 69(1): 9-24.
[15] Dornier, F. and Queruel, M. 2000. Weather Derivatives Pricing: Caution to the Wind. Energy & Power Risk Management, : 30-32.
[16] Duffie, D. and Richardson, H. 1991. Mean-Variance Hedging in Continuous Time. Annals of Applied Probability, 1: 1-15. · Zbl 0735.90021
[17] El Karoui, N. and Quenez, M. 1995. Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market. SIAM Journal on Control and Optimization, 33: 29-66. · Zbl 0831.90010
[18] Eydeland, A. and Geman, H. 1999. Pricing Power Derivatives. Risk, : 71-74.
[19] Follmer, H. and Leukert, P. 1999. Quantile Hedging. Finance and Stochastics, 3: 251-73. · Zbl 0977.91019
[20] Follmer, H. and Leukert, P. 2000. Efficient Hedging: Cost versus Shortfall Risk. Finance and Stochastics, 4: 117-46. · Zbl 0956.60074
[21] Follmer, H. and Sondermann, D. 1986. “Hedging of Non-redundant Contingent Claims”. In Contributions to Mathematical Economics, Amsterdam: North-Holland. · Zbl 0663.90006
[22] Gerber, H. U. and PafUmi, G. 1998. Utility Functions: From Risk Theory to Finance. North American Actuarial Journal, 2(3): 74-100. · Zbl 1081.91511
[23] Golden, L., Wang, M. and Yang, C. 2007. Handling Weather Related Risks through Financial Markets: Considerations of Credit Risk, Basis Risk, and Hedging. Journal of Risk and Insurance, 74(2): 319-46.
[24] Golden, L., Yang, C. and Zou, H. 2009. “The Effectiveness of Using a Basis Derivative Hedging Strategy to Mitigate the Financial Consequences of Weather-Related Risks”. In Working paper, University of Texas at Austin, Center for Risk Management and Insurance Research.
[25] Henderson, V. 2002. Valuation of Claims on Non-traded Assets Using Utility Maximization. Mathematical Finance, 12(4): 351-73. · Zbl 1049.91072
[26] Hirshleifer, D. and Shumway, T. 2003. Good Day Sunshine: Stock Returns and the Weather. Journal of Finance, 58(3): 1009-32.
[27] Hodges, S. and NeUberger, A. 1989. Optimal Replication of Contingent Claims under Transaction Costs. Review of Futures Markets, 8: 222-39.
[28] Kamstr, M., Kramer, L. and Levi, M. 2000. Losing Sleep at the Market: The Daylight-Savings Anomaly. American Economic Review, 12: 1005-1000.
[29] Lucas, R. 1978. Asset Prices in an Exchange Economy. Econometrica, 46: 1429-45. · Zbl 0398.90016
[30] Merton, R. 1969. Lifetime Portfolio Selection under Uncertainty: The Continuous Time Case. Review of Economics and Statistics, 51: 247-57.
[31] Merton, R. 1971. Optimum Consumption and Portfolio Rules in a Continuous-Time Model. Journal of Economic Theory, 3: 373-413. · Zbl 1011.91502
[32] Moller, T. 2003. Indifference Pricing of Insurance Contracts in a Product Space Model. Finance and Stochastics, 7(2): 197-217. · Zbl 1038.62097
[33] Moore, K. S. and Young, V. R. 2003. Pricing Equity-Linked Pure Endowments via the Principle of Equivalent Utility. Insurance: Mathematics and Economics, 33(3): 497-516. · Zbl 1103.91370
[34] Musiela, M. and Zariphopoulou, T. 2002. “Indifference Prices and Related Measures”. In Technical report, University of Texas at Austin.
[35] Owen, M. 2001. Utility Based Optimal Hedging in Incomplete Markets, Vienna, , Austria: University of Technology. Preprint
[36] Platen, E. and West, J. 2004. A Fair Pricing of Weather Derivatives. Asia-Pacific Financial Market, 11(1): 23-53. · Zbl 1075.91024
[37] Roll, R. 1984. Orange Juice and Weather. American Economic Review, 74(5): 861-80.
[38] Saunders, E. 1993. Stock Prices and Wall Street Weather. American Economic Review, 83(5): 1337-45.
[39] Schweizer, M. 1988. Hedging of Options in a General Semimartingale Model Zurich, , Switzerland Ph.D. diss., ETHZ no. 8615
[40] Schweizer, M. 1991. Option Hedging for Semimartingales. Stochastic Processes and Their Applications, 37: 339-63. · Zbl 0735.90028
[41] Sloan, D., Palmer, L. and Burrow, H. 2002. A Broker’s View. Global Reinsurance,
[42] Vukina, T., Li, D. and Holthausen, D. 1996. Hedging with Crop Yield Futures: A Mean-Variance Analysis. American Journal of Agricultural Economics, 78: 1015-25.
[43] Young, V. R. 2003. Equity-Indexed Life Insurance: Pricing and Reserving Using the Principle of Equavelent Utility. North American Actuarial Journal, 7(1): 68-86. · Zbl 1084.91521
[44] Young, V. R. and Zariphopoulou, T. 2002. Pricing Dynamic Insurance Risks Using the Principle of Equivalent Utility. Scandinavian Actuarial Journal, 4: 246-79. · Zbl 1039.91049
[45] Zariphopoulou, T. 2001. A Solution Approach to Valuation with Unhedgeable Risks. Finance and Stochastics, 5: 61-82. · Zbl 0977.93081
[46] Zeng, L. 2000. Pricing Weather Derivatives. Journal of Risk Finance, 1(3): 72-78.
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.