本文關(guān)鍵詞：美式期權(quán)定價(jià)的改進(jìn)的奇點(diǎn)分離法　出處：《西南財(cái)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(jià)問(wèn)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(lái)求解美式期權(quán)。美式期權(quán)定價(jià)問(wèn)題可以表示成一個(gè)熱方程的自由邊界問(wèn)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(lái)求解美式期權(quán)價(jià)格。因?yàn)槊朗狡跈?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(jì)算的結(jié)果比較精確,然而還是有不足之處,因?yàn)樗Ｓ械臄?shù)值計(jì)算方法一樣,確定計(jì)算域時(shí)都會(huì)取一個(gè)足夠大的值來(lái)保證足夠小的截?cái)嗾`差,然而這種做法使得許多格點(diǎn)上的計(jì)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(lái)避免無(wú)謂的計(jì)算過(guò)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(jì)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(lái)作為對(duì)比,我們采用二叉樹(shù)的計(jì)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(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F224;F830.91

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 吳志剛,金朝嵩;標(biāo)的股價(jià)服從混合過(guò)程的期權(quán)定價(jià)公式及有限元算法[J];經(jīng)濟(jì)數(shù)學(xué);2002年02期

，

本文編號(hào)：1384618