本文關(guān)鍵詞： 兩值期權(quán) 隨機(jī)利率 計(jì)價(jià)單位轉(zhuǎn)換 Girsanov定理 附息債券　出處：《南京師范大學(xué)》2013年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：近幾年,金融衍生品市場(chǎng)發(fā)展迅猛,尤其是期權(quán)的發(fā)展,對(duì)風(fēng)險(xiǎn)規(guī)避,風(fēng)險(xiǎn)投資和價(jià)值發(fā)現(xiàn)等金融領(lǐng)域產(chǎn)生了深遠(yuǎn)的影響。相應(yīng)的,期權(quán)定價(jià)也成為了金融數(shù)學(xué)最重要的部分之一。 目前,金融市場(chǎng)中產(chǎn)生了大量的新型衍生產(chǎn)品,兩值期權(quán)就是其中典型的一種,人們對(duì)利率是常數(shù)的情形下的兩值期權(quán)的定價(jià)問(wèn)題作了許多研究并得到了一些結(jié)果,但金融市場(chǎng)上,受多種因素影響,利率往往是一個(gè)隨機(jī)的變量。 在本篇論文中,主要通過(guò)無(wú)套利理論及轉(zhuǎn)換計(jì)價(jià)單位的方法,對(duì)隨機(jī)利率下兩值期權(quán)的定價(jià)問(wèn)題進(jìn)行了研究,主要的結(jié)果如下： (1)當(dāng)標(biāo)的資產(chǎn)是股票時(shí),本文分別討論了一維和多維情形下,兩值期權(quán)的定價(jià)問(wèn)題,給出了定價(jià)公式,同時(shí),討論了隨機(jī)利率情形下,兩值期權(quán)與歐式看漲期權(quán)之間的關(guān)系,并通過(guò)該關(guān)系給出了隨機(jī)利率情形下,歐式看漲期權(quán)的定價(jià)公式。 (2)當(dāng)標(biāo)的資產(chǎn)是零息債券時(shí),本文給出了兩值期權(quán)的定價(jià)公式；當(dāng)標(biāo)的資產(chǎn)是附息債券時(shí),本文同樣給出了其定價(jià)方法。
[Abstract]:In recent years, the financial derivatives market has developed rapidly, especially the development of options, which has had a profound impact on the financial fields such as risk aversion, venture capital and value discovery. Option pricing has also become one of the most important parts of financial mathematics. At present, a large number of new derivatives have been produced in the financial market. Two-valued option is one of the typical ones. People have done a lot of research and got some results on the pricing of two-valued options when the interest rate is constant. But in financial markets, interest rates are often a random variable affected by many factors. In this paper, the pricing problem of two-valued options under stochastic interest rate is studied by means of the no-arbitrage theory and the method of converting pricing units. The main results are as follows:. 1) when the underlying asset is a stock, this paper discusses the pricing problem of two-valued options under one-dimensional and multi-dimensional cases, and gives the pricing formula. At the same time, the relationship between two-valued options and European call options is discussed in the case of stochastic interest rate. Through this relation, the pricing formula of European call option is given. 2) when the underlying asset is a zero interest bond, this paper gives the pricing formula of the two-valued option, and when the underlying asset is an interest-bearing bond, the pricing method is also given in this paper.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類(lèi)號(hào)】：F224;F830.9

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本文編號(hào)：1505443