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  本文關(guān)鍵詞：單因子利率模型下的外匯期權(quán)定價(jià)　出處：《西南財(cái)經(jīng)大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 歐式外匯期權(quán) 單因子利率模型 遠(yuǎn)期變量變換 B-S公式

【摘要】：金融衍生品定價(jià)是金融領(lǐng)域內(nèi)的一大重要問題,實(shí)際應(yīng)用價(jià)值很大,同時(shí)又有極大的理論意義。外匯期權(quán)即是一種較為復(fù)雜的金融衍生工具,在我國市場(chǎng)上也是新近出現(xiàn)。我國現(xiàn)有的外匯期權(quán)產(chǎn)品都比較簡(jiǎn)單,對(duì)其主要是處在摸索階段,特別是距發(fā)達(dá)國家成熟的外匯期權(quán)體系還相差甚遠(yuǎn),所以此時(shí)對(duì)外匯期權(quán)的定價(jià)問題進(jìn)行一些探索和研究是很有必要的。本文即是研究了單因子利率模型下歐式外匯期權(quán)的合理定價(jià)問題。 期權(quán)是一種金融衍生產(chǎn)品,它的定價(jià)模型主要取決于原生資產(chǎn)的價(jià)格演化模型。在連續(xù)時(shí)間情形下,原生資產(chǎn)的價(jià)格演化可以表述為一個(gè)隨機(jī)微分方程,作為原生資產(chǎn)衍生物的期權(quán)的定價(jià)問題在此基礎(chǔ)上就可以變?yōu)橐粋�(gè)偏微分方程的定解問題。因此,研究期權(quán)定價(jià)的主要思路便是把偏微分方程作為工具,利用偏微分方程的理論和方法,建立起期權(quán)定價(jià)的數(shù)學(xué)模型,就能得出期權(quán)的定價(jià)公式,還可對(duì)期權(quán)的價(jià)格結(jié)構(gòu)做定性分析。本文即是沿著這個(gè)思路展開的。首先,在單因子利率模型下,給出了外匯期權(quán)的相關(guān)假設(shè)條件,再得到在假設(shè)條件下的歐式外匯期權(quán)所需滿足的偏微分方程,此方程主要是運(yùn)用鞅表示定理得到的。其次,就是對(duì)得到的偏微分方程進(jìn)行求解,此方程為三維形式,直接求解較復(fù)雜,本文就先利用遠(yuǎn)期變量變換降低了偏微分方程狀態(tài)空間的維數(shù),將方程轉(zhuǎn)化為普通的一維形式的邊界問題。再次,得出期權(quán)的定價(jià)公式。這里,運(yùn)用B-S公式就解出了相應(yīng)的歐式看漲和看跌外匯期權(quán)的顯式解。最后,本文還根據(jù)得出的歐式外匯期權(quán)的定價(jià)公式對(duì)影響其價(jià)格的因素進(jìn)行了敏感性分析,聯(lián)系實(shí)際,從側(cè)面佐證了定價(jià)公式的正確性。
[Abstract]:The pricing of financial derivatives is an important problem in the field of finance, which has great practical application value and great theoretical significance. Foreign exchange option is a more complex financial derivative instrument. The existing foreign exchange option products in China are relatively simple, mainly in the exploratory stage, especially far from the mature foreign exchange options system in developed countries. Therefore, it is necessary to explore and study the pricing of foreign exchange options. In this paper, we study the rational pricing of European foreign exchange options under the single-factor interest rate model. Option is a kind of financial derivative, its pricing model mainly depends on the price evolution model of the original asset. In the case of continuous time, the price evolution of the original asset can be expressed as a stochastic differential equation. On this basis, the pricing problem of options as a derivative of original assets can be transformed into a definite solution of partial differential equation. Therefore, the main idea of studying option pricing is to use partial differential equation as a tool. By using the theory and method of partial differential equation, the mathematical model of option pricing can be established and the option pricing formula can be obtained. The price structure of options can also be qualitatively analyzed. This paper starts with this idea. First of all, under the single-factor interest rate model, the relevant assumptions of foreign exchange options are given. Then we obtain the partial differential equation of the European foreign exchange option under the hypothetical condition. This equation is mainly obtained by using martingale representation theorem. Secondly, the obtained partial differential equation is solved. This equation is a three-dimensional form, the direct solution is more complex, this paper first use the forward variable transformation to reduce the dimension of the state space of partial differential equations, and transform the equation into the ordinary one-dimensional boundary problem. Here, using B-S formula to solve the corresponding European call and put foreign exchange options explicit solution. Finally. According to the European foreign exchange option pricing formula, this paper also analyzes the sensitivity of the factors affecting the price of the foreign exchange option, connecting with the practice, it proves the correctness of the pricing formula from the side.
【學(xué)位授予單位】：西南財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：F832.6;F224

【引證文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 張煜乾;帶隨機(jī)波動(dòng)的跳擴(kuò)散外匯期權(quán)定價(jià)模型及其應(yīng)用[D];安徽大學(xué);2013年

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本文編號(hào)：1410582