Valuation and Risk Management of Weather Derivatives: The Application of CME Rainfall Index Binary Contracts

Abstract

In this paper, we explore and analyze the valuation and risk management of rainfall index binary contracts, a type of precipitation derivative issued by the Chicago Mercantile Exchange (CME). We describe the underlying rainfall index with the occurrence model, which is built on a first-order, two-state Markov chain, and with the magnitude model based on mixed exponential distribution. To capture the seasonality characteristics, we describe the parameters of these two models with the truncated Fourier series. Since the weather derivatives market is incomplete due to the essence of its product, we value the rainfall index binary options with the Esscher transform and calibrate the market price of risk (MPR) with real market data. After analyzing the temporal behavior of the MPR, we find that the investors could have more accurate estimations of the rainfall index when approaching the end of the contract period or when entering the accumulation period. We also find that rather than speculators, the market participants are mainly hedgers, which may explain the shrinking of the precipitation derivatives market.

本文探索並分析了芝加哥商品交易所（CME）發行之雨量衍生性商品－雨量指數二元式合約的評價與風險管理。作為標的之雨量指數由兩種模型所刻畫：以一階兩狀態馬可夫鏈建立的降雨發生模型，以及以混合指數分配建立的雨量強度模型。上述兩模型之參數均以截斷傅立葉級數擬合，以捕捉降雨的季節性特徵。鑒於天氣衍生性商品市場之不完備性（肇因於商品本質），本文利用Esscher變換對選擇權進行評價，並以CME之真實市場價格校準獲得市場風險價格。在進一步分析市場風險價格的時間行為後，本文發現雨量指數二元式合約之市場參與者會隨著合約到期時間迫近或進入契約的累積期間，而對標的指數有著日益準確的估計；另本研究也發現這個市場的參與者大多為避險者而非投機者，這或許能解釋雨量衍生性商品市場萎縮的原因。