由於天氣異常變化的情況越來越劇烈，很多與天氣緊密相連的產業，營收也因而受到極大損失，因此利用天氣衍生性金融商品規避天氣風險所造成的損失開始受到企業界的重視，故對天氣衍生性金融商品定價也成為一項重要的議題，因為唯有能準確地對天氣衍生性金融商品定價，才能合理的預測天氣衍生性金融商品的未來價格，企業也才可作出正確的避險策略，這也是為何本文想對天氣衍生性商品定價。本文主要的研究目標，是利用無套利理論，估計最適的風險中立測度來定價天氣衍生性金融商品。但天氣衍生性金融商品的標的資產具有不可交易之特性，許多文獻皆指出這類商品存在非唯一之風險中立測度，卻少有文獻探討造成此現象的原因，因此探討造成天氣衍生性金融商品存在許多風險中立測度的原因是本文的第一個研究重點。此外因為以預期效用極大化原理評價天氣衍生性金融商品是一種常見的定價方法，但在此方法下就無考量風險中立測度的問題，因此本研究的第二個研究重點是藉由探討效用函數與風險中立測度間的關聯性來釐清此問題，並藉以說明為何本研究選擇利用無套利理論，估計最適的風險中立測度來天氣衍生性金融商品定價。本研究最後一個重點則是比較不同估計風險中立測度的作法，然後選擇一個較合理的方法估計風險中立測度，並利用此方法定價天氣衍生性金融商品。

Many weather-sensitive industries have experienced great losses due to the increases in extreme weather events, which inducing more and more enterprises to use weather derivatives to hedge their weather-related risks. Besides, only for pricing weather derivatives accurately can we predict the price of weather derivatives reasonably, enterprises, therefore, can make the right hedging strategy. Thus, the primary interest of this thesis is to price weather derivatives. Specifically, I apply no-arbitrage theory and the optimal estimated risk-neutral measure to value weather derivatives. Many have argued that weather derivatives have no unique risk-neutral measures due to their non-tradable feature. However, little literature has addressed the causes of no unique risk-neutral measures. In this thesis, my first goal is to explore the possibilities of these causes. In addition, I incorporate the expected utility theory and analyze the relationship between the utility functions and risk-neutral measures. By doing so, I can explain why I apply no-arbitrage theory and the optimal estimated risk-neutral measure to value weather derivatives. At the end, I compare various approaches of estimating risk-neutral measures, and value the weather derivatives accordingly.

[1] Alaton, P., Djehiche, B. and D. Stillberger (2002), “On modeling and pricing weather derivatives.” Appl. Math. Finance, vol.9, pp.1-20.

[2] Ansel, J.P. and C. Stricker (1992), “Lois de martingales, densites et decomposition de Fo ̈llmer Schweizer.” Annales de l’Institut H. Poincare, vol.28, pp. 375-392.

[3] Benth, F.E., S ̌altyte ̇-Benth, J. and S. Koekebakker (2007), “The volatility of temperature and pricing of weather derivatives.” Quantitative Finance.

[4] Brody, D., Syroka, J. and M. Zervos (2002), “Dynamical pricing of weather derivatives.” Quant. Finance, vol.3, pp.189-198.

[5] C ̌erny ́, A. (2009), “Arbitrage and pricing in the one-period model.” Mathematical techniques in finance, pp.41-47.

[6] Campbell, S.D. and F.X. Diebold (2005), “Weather forecasting for weather derivatives.” J. Amer. Statist. Assoc, vol.100, pp.6-16.

[7] Challis, S. (1999), “Forecast for profits.” Reactions.

[8] Davis, M.H.A. (1994), “A general option pricing formula.” Preprint Imperial College, London.

[9] Dornier, F. and M. Querel (2000), “Caution to the wind.” Energy Power Risk Manag., Weather risk special report, August, pp.30-32.

[10] Fo ̈llmer, H. and D. Sondermann (1986), “Hedging of non-redundant contingent claims.” Contributions to Mathematical Economics.

[11] Fo ̈llmer, H. and M. Schweizer (1991), “Hedging of contingent claims under incomplete information.” Applied Stochastic Analysis, Stochastics Monographs, vol.5, Gordon and Breach, London / New York.

[12] Frittelli, M. (1995), “Minimal entropy criterion for pricing in one period incomplete market.” Working Paper, Dip. Met. Quant., Univ. of Brescia, Italy.

[13] Ha ̈rdle, W.K. and B.L. Cabrera (2009), “Implied market price of weather risk.” Economic risk.

[14] Hamisultan, H. (2006), “Extracting information from the market to price the weather derivatives.” EconomiX.

[15] Hanley, M. (1999), “Hedging the force of nature.” Risk professional, pp.21-25.

[16] Hung, M.W. and Y.H. Liu (2006), “Valuation of weather derivatives.” Journal of financial studies, vol.14, No.1.

[17] Jackwerth, J.C. and M. Rubinstein (1996), “Recovering probability distributions from option prices.” Journal of finance, vol.51, No.5, 1611-1631.

[18] Karatzas, I. (1989), “Optimization problem in the theory of continuous trading.” Control and Optimization, vol.27, pp.1221-1259.

[19] Karatzas, I., Lehoczky, J.P., Shreve, S.E. and G.L. XU (1991), “Martingale and duality methods for utility maximization in an incomplete market.” SIAM J. Control and Optimization, vol.29, No.3, pp.702-730.

[20] Kramkov, D. and W. Schachermayer (1999), “The asymptotic elasticity of utility functions and optimal investment in incomplete markets.” The Annals of Applied Probability , vol.9, No.3, pp.904-950.

[21] Staum, J. (2007), “Incomplete markets.” Handbooks in operations research and management science, vol.15, pp.511-563.