本文關(guān)鍵詞： 期權(quán)定價(jià) 雙指數(shù)跳躍擴(kuò)散 雙障礙期權(quán) 拉普拉斯變換　出處：《山東大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

【摘要】：作為一種非常重要的金融衍生產(chǎn)品,期權(quán)從一出現(xiàn)就成為金融領(lǐng)域的研究熱點(diǎn),期權(quán)定價(jià)理論成為現(xiàn)代金融學(xué)理論的核心內(nèi)容之一,吸引了無(wú)數(shù)專家學(xué)者的注意。1973年,Fischer Black和Myron Scholcs提出了著名的Black-Scholcs期權(quán)定價(jià)模型[1],成為了金融衍生產(chǎn)品定價(jià)領(lǐng)域的基石。然而Black-Scholes模型是建立在非常理想的市場(chǎng)假設(shè)之下的,與現(xiàn)實(shí)情況不符,實(shí)際情況下市場(chǎng)存在的不確定因素有很多,因此許多學(xué)者在此模型的基礎(chǔ)上從不同角度對(duì)它進(jìn)行了推廣。從實(shí)證的角度考察,Black-Scholcs模型有兩個(gè)缺陷,一個(gè)是波動(dòng)率微笑,另一個(gè)是非對(duì)稱的尖峰厚尾現(xiàn)象。為了解釋這兩個(gè)現(xiàn)象很多學(xué)者提出了不同的模型。其中S.G.Kou于2002年提出了雙指數(shù)跳躍擴(kuò)散模型(DEJ)[2],對(duì)以上兩個(gè)實(shí)際中出現(xiàn)的現(xiàn)象做出了合理的解釋,此外該模型除了能給出普通期權(quán)的解析表達(dá)式,還能給出一些奇異期權(quán),比如障礙期權(quán)(barrier option)、回溯期權(quán)(lookback option)的解析定價(jià)公式。 本文介紹了經(jīng)典的Black-Scholcs模型,給出了標(biāo)的資產(chǎn)服從雙指數(shù)跳擴(kuò)散的歐式看漲期權(quán)的定價(jià)。之后介紹了雙指數(shù)跳躍擴(kuò)散模型下的障礙期權(quán)定價(jià)。然后我們用一種新的方法,利用拉普拉斯變換給出了雙指數(shù)跳躍擴(kuò)散模型下的雙障礙期權(quán)的解析定價(jià)公式。文章最后探討了歐式看漲期權(quán)定價(jià)模型參數(shù)的敏感性,對(duì)國(guó)內(nèi)市場(chǎng)上存在的一只權(quán)證進(jìn)行的研究,得出了比經(jīng)典的Black-Scholcs模型更好結(jié)果。
[Abstract]:As a very important financial derivative product, option has become a hot research topic in the field of finance since it appeared. Option pricing theory has become one of the core contents of modern finance theory. In 1973, Fischer Black and Myron Scholcs put forward the famous Black-Scholcs option pricing model [1], which became the cornerstone of the field of financial derivatives pricing. However, the Black-Scholes model is based on very ideal market assumptions. Contrary to the reality, there are many uncertain factors in the market, so many scholars generalize it from different angles on the basis of this model. There are two defects in Black-Scholcs model from the empirical point of view. One is the volatility smile, In order to explain these two phenomena, many scholars put forward different models. In 2002, S.G. Kou put forward a double exponential jump diffusion model (DEJ) [2]. There is a reasonable explanation. In addition, the model can not only give the analytic expressions of ordinary options, but also give some analytic pricing formulas for some strange options, such as barrier options, backtracking options, and lookback options. In this paper, the classical Black-Scholcs model is introduced, and the pricing of European call options with the diffusion of underlying assets from the double exponential jump is given. Then, the pricing of barrier options under the double exponential jump diffusion model is introduced. Then we use a new method. By using Laplace transform, the analytical pricing formula of double barrier options under the double exponential jump diffusion model is given. Finally, the sensitivity of the parameters of the European call option pricing model is discussed. The research on a warrant in the domestic market shows a better result than the classical Black-Scholcs model.
【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F224;F830.91

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本文編號(hào)：1512531