【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,對其進行有效的定價也顯得尤為重要.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)在許多方面與標準期權(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)到期日的某一時間決定此期權(quán)是看漲期權(quán)還是看跌期權(quán),此時間之后即為標準歐式期權(quán).任選期權(quán)能有效防范風(fēng)險,降低持有者的投資成本.因此,如何對任選期權(quán)進行合理有效的定價已成為現(xiàn)在研究的熱點話題.本文主要是對復(fù)雜任選期權(quán)進行定價.首先假設(shè)股票價格服從連續(xù)廣義指數(shù)O-U過程模型,無風(fēng)險利率以及股票價格的期望回報率、波動率均為時間的函數(shù),用鞅方法和保險精算方法分別給出了復(fù)雜任選期權(quán)在任意時刻t的價格的解析解.然而,在實際金融市場中股票價格會突然出現(xiàn)跳躍,連續(xù)過程無法準確刻畫股票價格的波動.因此,本文又假設(shè)股票價格服從跳擴散廣義指數(shù)O-U過程模型,更加準確的刻畫了股票價格波動的實際情況,并再次用鞅方法和保險精算方法分別給出了復(fù)雜任選期權(quán)在任意時刻t的價格的解析解.
[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

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