【摘要】：本文主要研究在常數(shù)波動率與隨機波動率下一維與多維美式勒式期權(quán)的定價問題。歐式的勒式期權(quán)相當(dāng)于一個歐式看漲期權(quán)和一個歐式看跌期權(quán)的組合,而美式的勒式期權(quán)由于其提前執(zhí)行的特性,導(dǎo)致了其價值與最佳實施邊界不同于一個美式看漲期權(quán)和一個美式看跌期權(quán)的組合,并且迄今為止,對美式勒式期權(quán)的研究還不充分。由于美式期權(quán)可在到期日前任意時刻實施,導(dǎo)致其定價不像歐式期權(quán)一樣存在一個顯式定價公式,因此需要使用數(shù)值方法求解。本文使用了叉樹方法和最小二乘蒙特卡洛方法計算常數(shù)波動率和隨機波動率下的一維和多維美式勒式期權(quán),并且給出了其最佳實施邊界。 首先,本文闡述了選題背景和意義。美式期權(quán)由于其可提前執(zhí)行的特點,成為金融市場中最活躍的期權(quán)交易類型。在美式期權(quán)這一類型中涌現(xiàn)了大量的交易品種,如亞式,回望式,蝶式,勒式等。其中美式勒式期權(quán)由于還未開始交易,因此相關(guān)研究文獻(xiàn)比較少。但是美式勒式期權(quán)其適合新興金融市場的特點在未來的應(yīng)用前景必然十分廣泛,歐式的勒式期權(quán)(勒式組合)已經(jīng)成為期權(quán)交易者的必備策略之一,美式勒式期權(quán)的產(chǎn)品研發(fā)上市只是時間的問題。研究美式勒式期權(quán)的定價問題,無論在交易市場上還是學(xué)術(shù)上,都非常有意義。本文希望能夠通過研究,豐富對勒式期權(quán)的認(rèn)識,為期權(quán)研究做出一些貢獻(xiàn)。 其次,本文核心內(nèi)容可分為三個部分,第一部分為常數(shù)波動率下的美式勒式期權(quán)的定價研究,第二部分為隨機波動率下的美式勒式期權(quán)的定價研究,第三部分為多維美式勒式期權(quán)的定價研究。 最后,本文給出了結(jié)論以及對文章進(jìn)一步研究的展望。
[Abstract]:In this paper, we study the pricing of one-dimensional and multi-dimensional American-type options under constant volatility and stochastic volatility. The European option is equivalent to the combination of a European call option and a European put option, while the American Le option has the characteristics of early execution. It leads to the difference between the value and the optimal implementation boundary of an American call option and an American put option, and so far, the research on the American Le option is not sufficient. Because the American option can be implemented at any time before the expiration date, the pricing of American option does not have an explicit pricing formula as that of European option, so it needs to be solved by numerical method. In this paper, the cross tree method and the least square Monte Carlo method are used to calculate the one dimensional multi dimensional American type option with constant volatility and random volatility, and the optimal implementation boundary is given. First of all, this paper expounds the background and significance of the topic. American option has become the most active option trading type in financial market because of its characteristics of early execution. A large number of American options have emerged in this type of trading, such as Asian, looking back, butterfly, and so on. Among them, the American-type option has not started trading, so the relevant research literature is relatively few. However, the characteristics of American type options which are suitable for emerging financial markets will be widely used in the future, and the European type of Le options has become one of the necessary strategies for option traders. It is only a matter of time before the R & D of American-style options is listed. It is very meaningful to study the pricing of American-type options both in the trading market and academically. This paper hopes to enrich the understanding of Le options and make some contributions to the study of options. Secondly, the core content of this paper can be divided into three parts: the first part is the pricing research of American type option under constant volatility, the second part is the study of American type option pricing under random volatility. The third part is the pricing of multi-dimensional American-type options. Finally, the conclusion and the prospect of further research are given.
【學(xué)位授予單位】：西南財經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F830.9;F224

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 鄧東雅;馬敬堂;單悅;;美式勒式期權(quán)定價問題研究[J];南方金融;2011年12期

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本文編號：2285967