本文選題：Bates模型 + 障礙期權(quán)�。� 參考：《廣西師范大學(xué)》2013年碩士論文

【摘要】：自20世紀(jì)60年代末,市場上出現(xiàn)障礙期權(quán)交易,障礙期權(quán)便發(fā)展迅速,口前,障礙期權(quán)的種類已超過數(shù)十種,障礙期權(quán)的出現(xiàn)給風(fēng)險(xiǎn)管理者們提供了更有效的方法,讓他們不必為他們認(rèn)為不可能到達(dá)的價(jià)格支付費(fèi)用。障礙期權(quán)的定價(jià)也自Fisher Black、Myron Scholes和Robert Merton在期權(quán)定價(jià)領(lǐng)域取得了重大突破之后,障礙期權(quán)在金融市場得到迅猛發(fā)展。其相對于標(biāo)準(zhǔn)的歐式、美式期權(quán),交易方式靈活、收益更符合投資者意愿、而且價(jià)格更加便宜,因此也更受投資者的喜愛。所以如何給這類奇異期權(quán)定價(jià)已成為金融數(shù)學(xué)領(lǐng)域研究的熱點(diǎn)課題之一。雖然經(jīng)典的Black-Sholes模型簡明、易于計(jì)算,但其過于理想化的假設(shè),使經(jīng)典的Black-Sholes模型在描述系統(tǒng)風(fēng)險(xiǎn)方面與觀測數(shù)據(jù)不符,因此人們不斷嘗試削弱Black-Sholes模型的假設(shè)條件,使之能更好的擬合金融數(shù)據(jù),大量實(shí)證研究表明：跳擴(kuò)散模型、隨機(jī)波動率模型在刻畫股價(jià)行為方面比經(jīng)典的Black-Sholes模型更符合實(shí)際,因此成為目前研究的前沿?zé)狳c(diǎn)課題,但在國內(nèi)外對Bates模型下障礙期權(quán)定價(jià)的研究成果并不多見。 障礙期權(quán)(Barrier Options)的終期收益不僅依賴于標(biāo)的資產(chǎn)到期日的價(jià)格,而且還依賴于標(biāo)的資產(chǎn)在整個(gè)合約有效期內(nèi)是否達(dá)到規(guī)定的障礙水平.由于它具有這種靈活的條款,因此其價(jià)格比標(biāo)準(zhǔn)期權(quán)便宜,并深受投資者的喜愛.本文將在Bates模型下,研究歐式、美式障礙期權(quán)定價(jià)。主要工作包括： 第一章介紹了期權(quán)定價(jià)以及本文的研究意義,國內(nèi)外對Bates模型下障礙期權(quán)定價(jià)的研究現(xiàn)狀,以及本文的選題依據(jù). 第二章在股票價(jià)格滿足Bates模型下討論離散時(shí)間情形的歐式障礙期權(quán)定價(jià),應(yīng)用半鞅Ito公式、多維隨機(jī)變量的特征函數(shù)、Girsanov測度變換以及Fourier反變換等隨機(jī)分析方法,給出離散時(shí)間情形的歐式障礙期權(quán)價(jià)格的顯示解,并利用數(shù)值計(jì)算分析了障礙期權(quán)價(jià)格受波動率參數(shù)的影響. 第三章在第二章Bates市場模型下討論美式期權(quán)及美式障礙期權(quán)定價(jià),首先研究美式期權(quán)定價(jià),先用3點(diǎn)G-J法對百慕大期權(quán)進(jìn)行分析,在得出美式期權(quán)定價(jià),其思想來自Geske和Johnson的分析.在用2點(diǎn)G-J法對百慕大障礙期權(quán)進(jìn)行離散化處理對其進(jìn)行定價(jià),進(jìn)而對美式障礙期權(quán)進(jìn)行定價(jià),最后進(jìn)行了數(shù)值計(jì)算且對結(jié)果進(jìn)行了分析. 第四章總結(jié)本文的主要工作和有待進(jìn)一步研究的問題.
[Abstract]:Since the late 1960s, barrier options have developed rapidly in the market, and the types of barrier options have exceeded dozens. The emergence of barrier options has provided more effective methods for risk managers. So they don't have to pay for prices they don't think they can reach. The pricing of barrier options has also developed rapidly in the financial market since the breakthrough in the field of option pricing made by Fisher Black-Myron Scholes and Robert Merton. Compared to standard European and American options, they are more flexible, more profitable and cheaper, and therefore more popular with investors. So how to price this kind of strange option has become one of the hot topics in the field of financial mathematics. Although the classical Black-Sholes model is simple and easy to calculate, it is too idealized to make the classical Black-Sholes model inconsistent with the observed data in describing the system risk. Therefore, people are constantly trying to weaken the hypothetical conditions of the Black-Sholes model. A large number of empirical studies show that the jump diffusion model and the stochastic volatility model are more practical than the classical Black-Sholes model in describing the behavior of stock price. However, there are few researches on barrier option pricing under Bates model at home and abroad. Barrier options (Barrier options) depends not only on the maturity price of the underlying asset, but also on whether the underlying asset reaches the specified barrier level during the whole term of the contract. Because of its flexible terms, it is cheaper than standard options and popular with investors. This paper will study the pricing of European and American barrier options under Bates model. The main tasks include: The first chapter introduces the option pricing and the significance of this paper, the domestic and foreign research status of barrier option pricing under the Bates model, as well as the basis of this paper. In chapter 2, we discuss the pricing of European barrier options with discrete time under the Bates model of stock prices. We apply the semi-martingale Ito formula, the eigenfunction of multidimensional random variables, the Girsanov measure transformation, and the Fourier inverse transformation. The explicit solution of the price of European barrier options in discrete time is given, and the influence of volatility parameters on the price of barrier options is analyzed by numerical calculation. The third chapter discusses the pricing of American options and American barrier options under the second chapter of Bates market model. Firstly, the pricing of American options is studied, and the Bermuda option is analyzed with the three-point G-J method, and the pricing of American options is obtained. Its thought comes from the analysis of Geske and Johnson. In this paper, a 2-point G-J method is used to discretize Bermuda barrier options to price them, and then American barrier options are priced. Finally, numerical calculations are carried out and the results are analyzed. The fourth chapter summarizes the main work of this paper and the problems to be further studied.
【學(xué)位授予單位】：廣西師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F830.9;F224;O211.6

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