本文關(guān)鍵詞：美式期權(quán)定價的改進(jìn)的奇點(diǎn)分離法　出處：《西南財經(jīng)大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 美式期權(quán) 自由邊界 有限差分 奇點(diǎn)分離

【摘要】：美式期權(quán)的定價問題一直是熱點(diǎn),由于它的解析解很難得出,因此,眾多學(xué)者都熱衷于尋找一種既有效又精確的數(shù)值方法來求解美式期權(quán)。美式期權(quán)定價問題可以表示成一個熱方程的自由邊界問題,而這種轉(zhuǎn)換也產(chǎn)生了許多不同的數(shù)值方法。 在本文中,我們將介紹一種有限差分?jǐn)?shù)值算法來求解美式期權(quán)價格。因為美式期權(quán)和歐式期權(quán)都滿足BS方程,它們的差也滿足轉(zhuǎn)換后的BS方程,根據(jù)這一特性,已經(jīng)有學(xué)者研究出奇點(diǎn)分離法,使得初始邊界條件為零,消除了奇點(diǎn)影響。奇點(diǎn)分離法計算的結(jié)果比較精確,然而還是有不足之處,因為它跟常有的數(shù)值計算方法一樣,確定計算域時都會取一個足夠大的值來保證足夠小的截斷誤差,然而這種做法使得許多格點(diǎn)上的計算值都是多余的。有學(xué)者就根據(jù)BS偏微分方程的性質(zhì)制造人工邊界來避免無謂的計算過程。 本文中介紹的方法將在奇點(diǎn)分離法的基礎(chǔ)上,引入人工邊界條件,計算的結(jié)果也表明結(jié)合的方法比奇點(diǎn)分離法要精確。其中為了得到精確解來作為對比,我們采用二叉樹的計算結(jié)果作為參考。
[Abstract]:The pricing of American option has always been a hot topic, because its analytical solution is very difficult to come out, so. Many scholars are keen to find an effective and accurate numerical method to solve American option. The American option pricing problem can be expressed as a free boundary problem of heat equation. This conversion also produces many different numerical methods. In this paper, we will introduce a finite difference numerical algorithm to solve the American option price, because both American option and European option satisfy BS equation, their difference is also satisfied with the converted BS equation. According to this characteristic, some scholars have studied the singularity separation method, which makes the initial boundary condition zero and eliminates the singularity effect. The results of the singularity separation method are more accurate, but there are still some shortcomings. Because it takes a large enough value to ensure a small truncation error when determining the computational domain, as is often the case with numerical methods. However, this method makes the calculation values on many lattice points superfluous. Some scholars have made artificial boundaries according to the properties of BS partial differential equations to avoid the unnecessary calculation process. The method introduced in this paper will introduce artificial boundary conditions on the basis of the singular point separation method. The results of calculation also show that the combined method is more accurate than the singular point separation method. We use the result of binary tree as a reference.
【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】：2014
【分類號】：F224;F830.91

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本文編號：1384618