【摘要】：本文主要包括兩部分：第一部分分析了可轉(zhuǎn)換債券常用的基本定價(jià)模型Tsiveriotis-Fernands(以下簡稱TF)模型,給出了TF模型的理論推導(dǎo),并參照Ayache-Forsyth-Vetzal(以下簡稱AFV)模型對違約的處理方法,對TF模型進(jìn)行改進(jìn),得到一個(gè)新的可轉(zhuǎn)換債券定價(jià)模型,并給出相應(yīng)的數(shù)值分析,由數(shù)值分析可以看出新模型與AFV模型定價(jià)結(jié)果相近,從而從理論上說明了TF模型對可轉(zhuǎn)換債券分解的合理性;第二部分,在TF模型的基礎(chǔ)上,研究可轉(zhuǎn)換債券中的風(fēng)險(xiǎn)因子—希臘值(Delta, Gamma)的計(jì)算方法,從而達(dá)到風(fēng)險(xiǎn)管理的目的。 在可轉(zhuǎn)換債券定價(jià)模型中,因?yàn)榭赊D(zhuǎn)換債券涉及到提前行權(quán)的問題,故可轉(zhuǎn)換債券定價(jià)滿足變分不等式,求解希臘值也較復(fù)雜,我們引入懲罰函數(shù),對變分不等問題用偏微分方程問題近似,從而得到希臘值滿足的定解問題,得到一個(gè)較好的求解方法,計(jì)算結(jié)果表明,這一方法對Delta因子計(jì)算效果良好；對于Gamma因子,因?yàn)榉匠讨谐霈F(xiàn)δ函數(shù),計(jì)算結(jié)果與價(jià)值函數(shù)差分有差異。
[Abstract]:This paper mainly includes two parts: the first part analyzes the basic pricing model of convertible bonds, Tsiveriotis-Fernands (hereinafter referred to as TF) model, gives the theoretical derivation of TF model, and refers to the Ayache-Forsyth-Vetzal (hereinafter referred to as AFV) model to deal with default. By improving the TF model, a new convertible bond pricing model is obtained, and the corresponding numerical analysis is given. From the numerical analysis, it can be seen that the pricing results of the new model are similar to those of the AFV model. In the second part, on the basis of TF model, we study the calculation method of Greek value (Delta, Gamma), which is the risk factor in convertible bond, so as to achieve the purpose of risk management. In the pricing model of convertible bonds, because convertible bonds involve the problem of early exercise of rights, the pricing of convertible bonds satisfies variational inequalities, and it is also more complicated to solve the Greek value, so we introduce the penalty function. The variational inequality problem is approximated by the partial differential equation problem, and the definite solution problem satisfying the Greek value is obtained, and a better solution method is obtained. The calculation results show that this method has good effect on the calculation of the Delta factor, and for the Gamma factor, Because there is 未 function in the equation, the result of calculation is different from the difference of value function.
【學(xué)位授予單位】：蘇州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F830.91;F224

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本文編號：2230732