【摘要】：金融數(shù)學(xué)中的衍生證券定價(jià)是人們廣泛研究的問(wèn)題之一,這種證券的定價(jià)依賴于與其相關(guān)的其它證券的價(jià)值.金融期權(quán)屬于金融衍生證券范疇,期權(quán)主要應(yīng)用于投機(jī)和套期保值.套期保值的主要策略是,根據(jù)在現(xiàn)貨市場(chǎng)買賣情況,交易者可以在期貨市場(chǎng)尋求品種、數(shù)量相同,但具有相反價(jià)格方向的期貨合同,用來(lái)補(bǔ)償未來(lái)某時(shí)刻或者某段時(shí)間現(xiàn)貨價(jià)格變化而帶來(lái)的風(fēng)險(xiǎn).為了有效地規(guī)避此類風(fēng)險(xiǎn),準(zhǔn)確估計(jì)期權(quán)的未來(lái)價(jià)格將是非常重要的,此即期權(quán)定價(jià)問(wèn)題. 對(duì)于金融產(chǎn)品的定價(jià)問(wèn)題,利用風(fēng)險(xiǎn)中性假設(shè)的分析方法是一種常用的方法,風(fēng)險(xiǎn)中性概率的構(gòu)造是此方法的關(guān)鍵.準(zhǔn)確的估計(jì)或者近似風(fēng)險(xiǎn)中性概率對(duì)于求解此類問(wèn)題至關(guān)重要.在考慮無(wú)套利情形下,基于風(fēng)險(xiǎn)中性定價(jià)原理,利用三次樣條函數(shù)作為近似函數(shù)替代風(fēng)險(xiǎn)中性概率測(cè)度,建立一個(gè)期權(quán)定價(jià)的二次規(guī)劃模型,效果比較理想.但是此方法只考慮結(jié)點(diǎn)處的非負(fù)性,沒(méi)有考慮整體區(qū)間上函數(shù)非負(fù)性,進(jìn)而建立了結(jié)合半正定條件的二次規(guī)劃模型,保證了近似函數(shù)的整體非負(fù)性.我們認(rèn)為二次樣條函數(shù)依然具有此類性質(zhì),并提出了二次樣條函數(shù)作為近似函數(shù)的一個(gè)期權(quán)定價(jià)的二次規(guī)劃模型,進(jìn)而也引入了半正定性條件建立了滿足整體區(qū)間非負(fù)性的二次規(guī)劃模型. 我們將在第一章中介紹問(wèn)題的背景和發(fā)展概況,同時(shí)給出本文所需的一些基本概念.對(duì)于現(xiàn)有的模型及理論將在第二章給出.在第三章中,重點(diǎn)討論新構(gòu)建的兩個(gè)模型.第四章,一系列數(shù)值實(shí)驗(yàn)說(shuō)明了新模型的有效性；結(jié)論部分簡(jiǎn)要地介紹了本文所取得的主要成果.
[Abstract]:The pricing of derivative securities in financial mathematics is one of the widely studied problems. The pricing of these securities depends on the value of other securities related to them. Financial options belong to the category of financial derivative securities, which are mainly used in speculation and hedging. The main strategy of hedging is that, depending on the situation of buying and selling in the spot market, traders can seek varieties in the futures market in the same number, but have futures contracts with opposite price directions. Used to compensate for future changes in spot prices at some point or time. In order to avoid this kind of risk effectively, it is very important to accurately estimate the future price of options, which is called option pricing problem. For the pricing problem of financial products, the analysis method of risk neutral hypothesis is a common method, and the construction of risk neutral probability is the key of this method. Accurate estimation or approximate risk neutral probability is very important for solving this kind of problem. In the case of no arbitrage, based on the principle of risk neutral pricing, the cubic spline function is used as an approximate function to replace the risk neutral probability measure, and a quadratic programming model of option pricing is established. The result is satisfactory. However, this method only considers the nonnegativity of the nodes and does not consider the nonnegativity of the functions on the whole interval. Furthermore, a quadratic programming model combined with the semi-positive definite conditions is established, which ensures the global nonnegativity of the approximate function. We consider that quadratic spline function still has this kind of property, and propose a quadratic programming model for option pricing of quadratic spline function as an approximate function. Then the semi-positive definite condition is introduced to establish the quadratic programming model which satisfies the global interval nonnegativity. In the first chapter, we will introduce the background and development of the problem, and give some basic concepts needed in this paper. The existing models and theories will be given in the second chapter. In the third chapter, we focus on the two newly constructed models. In chapter 4, a series of numerical experiments show the validity of the new model, and the main results obtained in this paper are briefly introduced in the conclusion.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：F224;F830.9

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本文編號(hào)：2451739