【摘要】：期權(quán)作為一種金融衍生工具,在金融市場中扮演著十分重要的角色,對其進(jìn)行有效的定價(jià)也顯得尤為重要.近幾年,由于金融市場發(fā)展迅速,出現(xiàn)了許多新型期權(quán),這些期權(quán)在許多方面與標(biāo)準(zhǔn)期權(quán)發(fā)生變異,被稱為奇異期權(quán).任選期權(quán)就是奇異期權(quán)的一種,它允許期權(quán)持有者在早于期權(quán)到期日的某一時(shí)間決定此期權(quán)是看漲期權(quán)還是看跌期權(quán),此時(shí)間之后即為標(biāo)準(zhǔn)歐式期權(quán).任選期權(quán)能有效防范風(fēng)險(xiǎn),降低持有者的投資成本.因此,如何對任選期權(quán)進(jìn)行合理有效的定價(jià)已成為現(xiàn)在研究的熱點(diǎn)話題.本文主要是對復(fù)雜任選期權(quán)進(jìn)行定價(jià).首先假設(shè)股票價(jià)格服從連續(xù)廣義指數(shù)O-U過程模型,無風(fēng)險(xiǎn)利率以及股票價(jià)格的期望回報(bào)率、波動率均為時(shí)間的函數(shù),用鞅方法和保險(xiǎn)精算方法分別給出了復(fù)雜任選期權(quán)在任意時(shí)刻t的價(jià)格的解析解.然而,在實(shí)際金融市場中股票價(jià)格會突然出現(xiàn)跳躍,連續(xù)過程無法準(zhǔn)確刻畫股票價(jià)格的波動.因此,本文又假設(shè)股票價(jià)格服從跳擴(kuò)散廣義指數(shù)O-U過程模型,更加準(zhǔn)確的刻畫了股票價(jià)格波動的實(shí)際情況,并再次用鞅方法和保險(xiǎn)精算方法分別給出了復(fù)雜任選期權(quán)在任意時(shí)刻t的價(jià)格的解析解.
[Abstract]:As a kind of financial derivative, option plays a very important role in financial market. In recent years, due to the rapid development of the financial market, there are many new options, these options and standard options in many ways have changed, known as strange options. An optional option is one of the exotic options, which allows the holder of an option to decide whether the option is a call option or a put option at a time earlier than the expiration date of the option, after which time it is a standard European option. Optional options can effectively guard against risk and reduce the investment cost of the holder. Therefore, how to make reasonable and effective pricing of optional options has become a hot topic. This article mainly carries on the pricing to the complex optional option. First of all, assume that the stock price service from the continuous generalized index O-U process model, risk-free interest rate and the expected rate of return of stock prices, volatility is a function of time, By means of martingale method and actuarial method, the analytical solutions of the price of complex optional options at any time t are given respectively. However, in the actual financial market, the stock price will suddenly jump, continuous process can not accurately describe the volatility of stock prices. Therefore, this paper assumes the generalized index O-U process model of stock price from jump diffusion to describe the actual situation of stock price fluctuation more accurately. Then the analytical solution of the price of complex optional options at any time t is given by using martingale method and actuarial method respectively.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F830.9

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 朱霞;葛翔宇;;股票價(jià)格服從指數(shù)O-U跳擴(kuò)散過程的期權(quán)定價(jià)[J];統(tǒng)計(jì)與決策;2014年03期

2 鄧國和;;Heston模型的歐式任選期權(quán)定價(jià)與對沖策略[J];廣西師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年03期

3 牛淑敏;徐云;;分?jǐn)?shù)跳-擴(kuò)散運(yùn)動下歐式復(fù)雜任選期權(quán)定價(jià)[J];數(shù)學(xué)理論與應(yīng)用;2012年02期

4 張凱凡;;鞅方法在股指期權(quán)定價(jià)中的應(yīng)用[J];湖北工業(yè)大學(xué)學(xué)報(bào);2011年05期

5 王海葉;;參數(shù)隨時(shí)間變化的任選期權(quán)的定價(jià)公式[J];襄樊學(xué)院學(xué)報(bào);2011年05期

6 呂潔;;鞅方法在期權(quán)定價(jià)中的應(yīng)用[J];財(cái)經(jīng)界(學(xué)術(shù)版);2010年08期

7 王獻(xiàn)東;杜雪樵;;跳擴(kuò)散模型下的復(fù)合期權(quán)定價(jià)[J];數(shù)學(xué)的實(shí)踐與認(rèn)識;2009年14期

8 李美蓉;;隨機(jī)利率下股票價(jià)格服從指數(shù)O-U過程的期權(quán)定價(jià)[J];合肥工業(yè)大學(xué)學(xué)報(bào)(自然科學(xué)版);2009年04期

9 黃國安;鄧國和;霍海峰;;跳躍-擴(kuò)散過程下歐式任選期權(quán)的定價(jià)[J];山西大學(xué)學(xué)報(bào)(自然科學(xué)版);2008年03期

10 畢學(xué)慧;杜雪樵;;后定選擇權(quán)的保險(xiǎn)精算定價(jià)[J];合肥工業(yè)大學(xué)學(xué)報(bào)(自然科學(xué)版);2007年05期

，

本文編號：2340726