【摘要】：近幾年來(lái),隨著電力工業(yè)市場(chǎng)的改革,電力衍生品市場(chǎng)進(jìn)一步發(fā)展,許多普通電力期權(quán)以及一些奇異期權(quán)紛紛出現(xiàn),因此對(duì)這些期權(quán)的定價(jià)研究成為一個(gè)迫切的問(wèn)題。 電力是一種常見(jiàn)的資源,具有不可存儲(chǔ)的特性,這一特性就排除傳統(tǒng)的現(xiàn)貨市場(chǎng)上基于存儲(chǔ)的定價(jià)方法以及傳統(tǒng)的無(wú)套利原理來(lái)定價(jià)電力期權(quán)的方法,所以以電力期貨為標(biāo)的來(lái)復(fù)制電力衍生品的方法是必要的。本文主要描述了兩類電力期權(quán),一類是熱率相關(guān)期權(quán)(spark spread option),一類是區(qū)域傳輸期權(quán)(locational spread option),這兩類期權(quán)即服從幾何布朗運(yùn)動(dòng)又服從均值回復(fù)過(guò)程。文中采用基于電力期貨和無(wú)風(fēng)險(xiǎn)資產(chǎn)的復(fù)制方法建立偏微分方程,進(jìn)而通過(guò)計(jì)價(jià)單位轉(zhuǎn)換,得到熱率相關(guān)期權(quán)和區(qū)域傳輸期權(quán)的定價(jià)公式。另外,本文還提出了一種新的數(shù)值方法,通過(guò)在空間方向上運(yùn)用有限元方法,在時(shí)間方向上運(yùn)用有限差分法來(lái)求解熱率相關(guān)看漲期權(quán)的偏微分方程,最終得到服從幾何布朗運(yùn)動(dòng)情況下歐式熱率相關(guān)看漲期權(quán)的數(shù)值解,并采用空間逼近的不連續(xù)性獲得了熱率相關(guān)看漲期權(quán)的有限元解和真解間的誤差階,誤差階趨向于2。最終結(jié)論顯示,利用有限元方法得到的數(shù)值解和真解很逼近,可以相互替代,進(jìn)而體現(xiàn)了本文中提到的數(shù)值方法的重要性。
[Abstract]:In recent years, with the reform of the power industry market and the further development of the power derivatives market, many ordinary power options and some strange options have emerged, so the pricing of these options has become an urgent problem. Electricity is a kind of common resource, which can not be stored. This characteristic excludes the traditional spot market pricing method based on storage and the traditional method of pricing power option based on no arbitrage principle. Therefore, it is necessary to copy the electricity derivatives with electricity futures as the target. In this paper, two kinds of power options are described, one is heat rate dependent option (spark spread option), and the other is regional transmission option (locational spread option),. These two kinds of options are subjected to both geometric Brownian motion and mean recovery process. In this paper, the partial differential equation based on power futures and risk-free assets is established, and the pricing formulas of heat ratio related options and regional transmission options are obtained through unit conversion. In addition, a new numerical method is proposed to solve the partial differential equations of call options related to the heat rate by using the finite element method in the space direction and the finite difference method in the time direction. Finally, the numerical solution of Euclidean heat ratio dependent call option under geometric Brownian motion is obtained, and the error order between finite element solution and true solution of heat rate dependent call option is obtained by using spatial approximation discontinuity. The error order tends to be 2. The final conclusion shows that the numerical solution and the true solution obtained by the finite element method can be approximated and can be replaced each other, thus reflecting the importance of the numerical method mentioned in this paper.
【學(xué)位授予單位】：天津財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F830.9;F224;O241.82

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