Abstract
The prevalence of commercial activities whose profit and cost are correlated with weather risk makes weather derivatives valuable financial instruments that enable hedging of price or volumetric (quantity) risk in many industries. This paper proposes a multi-period equilibrium pricing model for weather derivative. In our stylized economy representative agents of weather-sensitive industries optimizes their hedging portfolios that drive the supply and demand for weather derivative which are dynamically determined based on a utility indifference pricing framework. At equilibrium the weather derivative market will be cleared and their market price can be obtained. Numerical examples illustrate the equilibrium prices and optimal choices for the weather derivative as function of the correlation between weather indices and demand for the underlying commodity. We also demonstrate the benefit of multiple trading opportunities which allows rebalancing of the hedging portfolio prior to the commodity delivery date, as compared to a single shot framework.
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References
Alaton, P., Djehiche, B., Stillberger, D.: On modelling and pricing weather derivatives. Appl. Math. Finance 9, 1–20 (2002)
Ankirchner, S., Imkeller, P., Popier, A.: Optimal cross hedging of insurance derivatives. Stoch. Anal. Appl. 26, 679–709 (2008)
Audet, N., Heiskanen, P., Keppo, J., Vehvilainen, I.: Modeling electricity forward curve dynamics in the Nordic market. In: Bunn, D.W. (ed.): Modelling Prices in Competitive Electricity Markets. Wiley Series in Financial Economics, pp. 251–265. Wiley, New York (2004)
Benth, F.: Arbitrage-free pricing of weather derivatives based on fractional Brownian motion. Appl. Math. Finance 10, 303–324 (2003)
Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–655 (1973)
Brockett, P.L., Wang, M.: Portfolio effects and valuation of weather derivatives. Financ. Rev. 41 (2006)
Brody, D., Syroka, J., Zervos, M.: Dynamic pricing of weather derivatives. Quant. Finance 2, 189–198 (2002)
Cao, M., Wei, J.: Pricing weather derivative: an equilibrium approach. J. Futures Mark. 24, 1065–1089 (2004)
Carr, P., Madan, D.: Optimal positioning in derivative securities. Quant. Finance 1, 19–37 (2001)
Chaumont, S., Imkeller, P., Muller, M., Horst, U.: A simple model for trading climate risk. Q. J. Econ. Res. 74 (2005)
Davis, M.: Pricing weather derivatives by marginal value. Quant. Finance 1, 305–308 (2001)
Frittelli, M.: The minimal entropy martingale measure and the valuation problem in incomplete markets. Math. Finance 10, 39–52 (2000)
Goll, T., Ruschendorf, L.: Minimal distance martingale measures and optimal portfolios consistent with observed market prices. Finance Stoch. 5, 557–581 (2001)
Hamisultane, H.: Extracting information from the market to price the weather derivatives. ICFAI J. Deriv. Mark. 4, 17–46 (2007)
Heath, D., Jarrow, R., Morton, A.: Bond pricing and the term structure of interest rates: a new methodology for contingent claim valuation. Econometrica 66, 77–105 (1992)
Jewson, S., Brix, A.: Weather Derivative Valuation. Cambridge (2005)
Jewson, S., Caballero, R.: Seasonality in the statistics of surface air temperature and the pricing of weather derivatives. Meteorol. Appl. 10, 367–376 (2003)
Jouini, E.: Arbitrage and control problems in finance: a presentation. J. Math. Econ. 35, 167–183 (2001)
Kroll, Y., Levy, H., Markowitz, H.M.: Mean-variance versus direct utility maximization. J. Finance 39(1), 47–61 (1984)
Lee, Y., Oren, S.S.: An equilibrium pricing model for weather derivatives in a multi-commodity setting. Energy Econ. 31, 702–713 (2009)
Li, X., Sailor, D.J.: Electricity use sensitivity and climate and climate change. World Resour. Rev. 3, 334–346 (1995)
Lucas, R.E.: Asset prices in an exchange economy. Econometrica 46, 1429–1445 (1978)
Merton, R.C.: Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4, 141–183 (1973)
Platen, E., West, J.: A fair pricing approach to weather derivatives. Asia-Pac. Financ. Mark. 11, 23–53 (2004)
Richards, T.J., Manfredo, M.R., Sanders, D.R.: Pricing weather derivatives. Am. J. Agric. Econ. 86 (2004)
Samuelson, P.A.: Lifetime portfolio selection by dynamic stochastic programming. Rev. Econ. Stat. 51, 239–246 (1969)
Schweizer, M.: Approximation pricing and the variance-optimal martingale measure. Ann. Probab. 24, 206–236 (1996)
Staum, J.: Fundamental theorems of asset pricing for good deal bounds. Math. Finance 14(2), 141–161 (2004)
Staum, J.: Incomplete Market. Elsevier, Amsterdam (2008), Chap. 12, pp. 511–563
Yamada, Y.: Valuation and hedging of weather derivatives on monthly average temperature. J. Risk 10 (2007)
Yoo, S.: Weather derivatives and seasonal forecast. Asia-Pac. J. Financ. Stud. 213–246 (2004)
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Lee, Y., Oren, S.S. A multi-period equilibrium pricing model of weather derivatives. Energy Syst 1, 3–30 (2010). https://doi.org/10.1007/s12667-009-0004-7
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DOI: https://doi.org/10.1007/s12667-009-0004-7