【摘要】：美式期權(quán)定價(jià)一直是期價(jià)定價(jià)方面研究得比較多的一個(gè)問(wèn)題,美式期權(quán)定價(jià)不同于歐式期權(quán)定價(jià),由于美式期權(quán)可以在到期日前提前執(zhí)行的特性,使得美式期權(quán)的定價(jià)要比歐式期權(quán)困難得多。再者由于美式期權(quán)以及其組合的多樣化,使得它的定價(jià)問(wèn)題更加復(fù)雜。本文考慮一種具有代表性的美式勒式期權(quán)來(lái)研究它的定價(jià)問(wèn)題。 本文主要從積分方程的角度來(lái)研究該期權(quán)的定價(jià)問(wèn)題。美式勒式期權(quán)的價(jià)值可以表示成EEP形式——期權(quán)值=歐式勒式期權(quán)的價(jià)值+提前執(zhí)行金。由此可以推出美式勒式期權(quán)的最佳執(zhí)行邊界滿足非線性奇異的Volterra積分方程組。 雖然在之前的文獻(xiàn)中有學(xué)者研究了美式勒式期權(quán)的最佳執(zhí)行邊界和價(jià)值(例如:Chiarella與Ziogas (2005)),但所用方法計(jì)算難度大,且精度只達(dá)到了小數(shù)點(diǎn)后四位。本文發(fā)展了積分方程數(shù)值解中的一種基于高階多項(xiàng)式的高精度配置方法,這種方法在計(jì)算數(shù)學(xué)中被廣泛使用,它能有效求解并實(shí)現(xiàn)非線性奇異的Volterra方程組,從而求出美式勒式期權(quán)的最佳執(zhí)行邊界和價(jià)值。 本文的算例與已存在的算法比較,充分顯示了高精度配置法精度高、易實(shí)現(xiàn)的特點(diǎn)。此外,高精度配置法所使用的逼近多項(xiàng)式的階數(shù)高,在節(jié)點(diǎn)處的導(dǎo)數(shù)連續(xù),更易求得希臘值,這是該方法的另一特點(diǎn)。
[Abstract]:American option pricing has always been a problem that has been studied in the pricing of futures. The pricing of American options is different from that of European options, because of the characteristics of American options that can be executed in advance of the expiration date. It makes American options much more difficult to price than European options. Moreover, because of the diversification of American option and its combination, the pricing problem of American option is more complicated. In this paper, we consider a representative American-type option to study its pricing problem. In this paper, the pricing of this option is studied from the angle of integral equation. The value of American type option can be expressed as EEP form-option value = European type option value. Thus, the optimal executive boundary of American type option can satisfy the nonlinear singular Volterra integral equations. Although some scholars have studied the optimal execution boundary and value of American type option (for example, Chiarella and Ziogas (2005), the method is difficult to calculate and the precision is only four decimal places. In this paper, a high precision collocation method based on higher order polynomials is developed for numerical solutions of integral equations. This method is widely used in computational mathematics. It can effectively solve and implement nonlinear singular Volterra equations. Thus, the optimal execution boundary and value of American-type options are obtained. Compared with the existing algorithms, the example of this paper fully shows the characteristics of high precision collocation method with high precision and easy to be realized. In addition, the order of approximation polynomial used in high precision collocation method is high, the derivative at the node is continuous, and it is easier to obtain Greek value, which is another characteristic of this method.
【學(xué)位授予單位】：西南財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：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(jià)問(wèn)題研究[J];南方金融;2011年12期

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本文編號(hào)：2344050