【摘要】：期權(quán)定價(jià)一直是金融數(shù)學(xué)、金融工程領(lǐng)域研究的核心問題之一.隨著金融市場的快速發(fā)展,以及金融公司、投資者對(duì)復(fù)雜金融衍生工具的喜愛,許多金融機(jī)構(gòu)不斷推出新型衍生產(chǎn)品,因此新型期權(quán)(也稱奇異型期權(quán))就隨之出現(xiàn)并得到了迅速發(fā)展.復(fù)合期權(quán)是最常見,應(yīng)用最廣泛的奇異期權(quán)中的一種.它是期權(quán)的期權(quán),所以有兩個(gè)到期日和兩個(gè)執(zhí)行價(jià)格.因?yàn)槭艿絻蓚�(gè)到期日的影響,與標(biāo)準(zhǔn)的期權(quán)相比,復(fù)合期權(quán)對(duì)波動(dòng)率更加敏感,導(dǎo)致其價(jià)值的判斷更加復(fù)雜.然而,在復(fù)雜多變的金融市場和發(fā)展時(shí)快時(shí)慢的經(jīng)濟(jì)環(huán)境下,傳統(tǒng)的Black-Scholes模型,跳擴(kuò)散模型以及單因素隨機(jī)波動(dòng)率模型已不再適用,因此,本文提出了在雙因素隨機(jī)波動(dòng)率跳擴(kuò)散模型下對(duì)復(fù)合期權(quán)進(jìn)行研究.本文從多因素角度出發(fā),全面考慮金融市場長期風(fēng)險(xiǎn)和短暫風(fēng)險(xiǎn)引起的波動(dòng)以及經(jīng)濟(jì)發(fā)展時(shí)快時(shí)慢的特征,綜合跳擴(kuò)散模型和隨機(jī)波動(dòng)率模型的優(yōu)點(diǎn),建立雙因素隨機(jī)波動(dòng)率跳擴(kuò)散模型.在該模型下首先運(yùn)用Feynman-Kac定理,Ito公式,多維隨機(jī)變量的聯(lián)合特征函數(shù)以及Fourier反變換等方法,推導(dǎo)出標(biāo)準(zhǔn)歐式復(fù)合期權(quán)定價(jià)公式.通過數(shù)值實(shí)例比較九類模型下復(fù)合期權(quán)價(jià)格隨S0的異動(dòng)情況,分析了短期、長期兩種不同到期日的隱含波動(dòng)率情況,以及短期、長期波動(dòng)率的跳躍強(qiáng)度和相關(guān)系數(shù)對(duì)復(fù)合期權(quán)價(jià)格的影響,發(fā)現(xiàn)該模型能更好的捕捉隱含波動(dòng)率期限結(jié)構(gòu)的時(shí)變特征,短期、長期波動(dòng)率的相關(guān)系數(shù)對(duì)復(fù)合期權(quán)價(jià)格都有正向的沖擊,并且在短期波動(dòng)率下復(fù)合期權(quán)價(jià)格波動(dòng)比較劇烈,而在長期波動(dòng)率下復(fù)合期權(quán)價(jià)格趨于更平穩(wěn)狀態(tài).其次在本文模型下將單期復(fù)合期權(quán)推廣到多期復(fù)合期權(quán)定價(jià),運(yùn)用多維隨機(jī)變量的聯(lián)合特征函數(shù)和多維傅里葉反變換方法,推導(dǎo)出多期復(fù)合期權(quán)定價(jià)公式.通過數(shù)值實(shí)例比較在Merton模型,SVIJ模型與本論文模型下多期復(fù)合期權(quán)的價(jià)格,分析了多期復(fù)合期權(quán)受短期波動(dòng)率相關(guān)參數(shù)的影響,發(fā)現(xiàn)跳躍項(xiàng)的加入和雙因素隨機(jī)波動(dòng)率的考慮對(duì)多期復(fù)合期權(quán)定價(jià)結(jié)果影響較大,并且短期波動(dòng)率相關(guān)參數(shù)對(duì)多期復(fù)合期權(quán)價(jià)格會(huì)造成不同沖擊.所以,在實(shí)際金融市場中,投資者不僅要關(guān)注長期波動(dòng)率,更應(yīng)該重視短期波動(dòng)率及其相關(guān)參數(shù)引起的股價(jià)波動(dòng).在雙因素隨機(jī)波動(dòng)率跳擴(kuò)散模型下研究復(fù)合期權(quán)定價(jià)問題更適用于現(xiàn)實(shí)金融市場,為復(fù)合期權(quán)定價(jià)研究提供更為有力的理論依據(jù)和方法,同時(shí)也為風(fēng)險(xiǎn)管理者能做出更有效的判斷提供了參考依據(jù)。
[Abstract]:Option pricing has always been one of the core issues in the field of financial mathematics and financial engineering. With the rapid development of financial markets and the love of financial companies and investors for complex financial derivatives, many financial institutions continue to launch new derivatives, so new options (also known as odd options) have emerged and developed rapidly. Compound option is one of the most common and widely used singular options. It is an option for an option, so there are two due dates and two execution prices. Because of the influence of two maturity dates, compared with the standard option, the compound option is more sensitive to volatility, which makes the judgment of its value more complex. However, in the complex and changeable financial market and the fast and slow economic environment, the traditional Black-Scholes model, jump diffusion model and single factor random volatility model are no longer applicable. Therefore, this paper proposes to study the compound option under the two factor random volatility jump diffusion model. From the point of view of many factors, this paper comprehensively considers the fluctuation caused by long-term risk and temporary risk in financial market and the characteristics of fast and slow economic development, and synthesizes the advantages of jump diffusion model and random volatility model, and establishes a two-factor random volatility jump diffusion model. Under this model, the standard European compound option pricing formula is derived by using Feynman-Kac theorem, Ito formula, joint eigenfunction of multidimensional random variables and Fourier inverse transformation. By comparing the variation of compound option price with S0 under nine kinds of models, this paper analyzes the implied volatility of two different maturity dates of short-term and long-term, and the influence of jump intensity and correlation coefficient of short-term and long-term volatility on the price of compound option. It is found that the model can better capture the time-varying characteristics of term structure of implied volatility. The correlation coefficient of long-term volatility has a positive impact on the price of composite options, and the price of composite options fluctuates violently under the short-term volatility, while the price of composite options tends to be more stable under the long-term volatility. Secondly, under the model of this paper, the single-period compound option is extended to the pricing of multi-period compound option, and the pricing formula of multi-period compound option is derived by using the joint characteristic function of multi-dimensional random variables and the method of multi-dimensional Fourier transform. Through the comparison of the prices of multi-period composite options under Merton model, SVIJ model and this model, this paper analyzes the influence of short-term volatility on the price of multi-period composite options. It is found that the addition of jump term and the consideration of two-factor random volatility have great influence on the pricing results of multi-period composite options, and the related parameters of short-term volatility will have different impacts on the price of multi-period composite options. Therefore, in the actual financial market, investors should not only pay attention to the long-term volatility, but also pay attention to the stock price volatility caused by the short-term volatility and its related parameters. The study of compound option pricing under the two-factor random volatility jump-diffusion model is more suitable for the real financial market, which provides a more powerful theoretical basis and method for the study of compound option pricing, and also provides a reference for risk managers to make more effective judgment.
【學(xué)位授予單位】：廣西師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F830.9;O211.6

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