Master-Arbeit Univ. St. Gallen, 2006.

近年來，能源商品的價格隨著國際政治情勢、國際金融環境以及景氣循環的影響產生劇烈波動，基於避險的需求，衍生性商品交易量也逐漸增加。然而，在評價能源衍生性商品的過程中，即期價格動態模型的選擇對於訂價與避險的結果有著顯著的影響，如何選擇一個適當的動態模型以評價能源商品便成為本文研究的目標。在指數與股價選擇權的評價模型中，大多以Black and Scholes (1973)提出的選擇權評價模型作為基礎，但Black-Scholes模型是否適用於評價能源市場的選擇權價格卻是有待商榷。Schwartz (1997)提出以均數回歸模型 (Mean Reversion Model)描述能源即期價格，發現比Black-Scholes模型中所假設的即期價格動態模型更能描述能源市場即期價格的波動。本研究也考慮能源市場遇到重大事件而造成即期價格產生劇烈波動的情況，因此在模型中加入跳躍項以捕捉價格跳躍的現象。另外，能源商品的需求與季節變化有高度相關性，因此本文亦考量即期價格的變動會受到季節性的變動影響，在模型中加入季節性函數，以補捉季節性的價格變化。基於前述模型考量，本研究在各種描述能源商品即期價格特性的動態模型之下，推導各個模型的期貨選擇權定價公式，進一步測試各模型在金融風暴與非金融風暴期間的訂價誤差與避險誤差，以提供投資人或避險需求者於原油期貨選擇權模型選用上之參考。 / In recent years, the price of energy commodities has fluctuated with the international political situation and the international financial environment. For the sake of hedging demands, the trading volume of derivatives has been gradually increasing. In the process of valuation of energy derivatives, choices of the spot price dynamics model have a significant impact on pricing and hedging. Therefore, how to choose an appropriate dynamic model to evaluate the energy commodities has been main purpose of this study. Two main models are tested in this paper. One is the option pricing model supposed by Black and Scholes (1973), and another is the mean reversion model supposed by Schwartz (1997). This study also considered the volatility of the spot price in the energy market in case of major events, so the researcher adds the jump to explore the mean reversion model. In addition, the demand for energy commodities is highly correlated with seasonal variations. The vibration of spot price often affected by the seasonal variations is considered in the research. Therefore, the researchers also take the seasonal function into the research to capture the seasonal price changes. Based on considerations described above, the pricing formula for each model of futures option is evaluated in the research. The researcher further tests the pricing errors and hedging errors of each model during the financial crises and non-financial crises in order to provide the investors and hedging demanders with some suggestions about selecting oil futures option models.

Zugl.: Oestrich-Winkel, Europ. Business School, Diss., 2008.

本文實證探討黃金期貨報酬率的特性並在標的黃金期貨價格遵循狀態轉換跳躍擴散過程時實現美式選擇權之評價。在這樣的動態過程下，跳躍事件被一個複合普瓦松過程與對數常態跳躍振幅所描述，以及狀態轉換到達強度是由一個其狀態代表經濟狀態的隱藏馬可夫鏈所捕捉。考量不同的跳躍風險假設，我們使用Merton測度與Esscher轉換推導出在一個不完全市場設定下的風險中立黃金期貨價格動態過程。為了達到所需的精確度，最小平方蒙地卡羅法被用來近似美式黃金期貨選擇權的價值。基於實際市場資料，我們提供實證與數值結果來說明這個動態模型的優點。 / This dissertation empirically investigates the characteristics of gold futures returns and achieves the valuation of American-style options when the underlying gold futures price follows a regime-switching jump-diffusion process. Under such dynamics, the jump events are described as a compound Poisson process with a log-normal jump amplitude, and the regime-switching arrival intensity is captured by a hidden Markov chain whose states represent the economic states. Considering the different jump risk assumptions, we use the Merton measure and Esscher transform to derive risk-neutral gold futures price dynamics under an incomplete market setting. To achieve a desired accuracy level, the least-squares Monte Carlo method is used to approximate the values of American gold futures options. Our empirical and numerical results based on actual market data are provided to illustrate the advantages of this dynamic model.