本文選題：Vasicek利率模型 + Girsanov定理　； 參考：《河北師范大學(xué)》2012年碩士論文

【摘要】：金融工程是一門比較系統(tǒng)的學(xué)科,它包括金融產(chǎn)品的設(shè)計(jì),金融產(chǎn)品的定價(jià),金融產(chǎn)品的交易策略以及金融風(fēng)險(xiǎn)的管理等各個(gè)方面.其中如何給金融產(chǎn)品定價(jià)是人們最為關(guān)注的重要問題之一.金融學(xué)家以及數(shù)學(xué)家們?yōu)閷で蠼鹑诋a(chǎn)品的合理定價(jià)進(jìn)行了大量的研究. 本文以先前研究成果為基礎(chǔ),對貼現(xiàn)債券上的復(fù)合期權(quán)的定價(jià)進(jìn)行了研究.考慮到貼現(xiàn)債券的價(jià)格波動與利率的波動密切相關(guān),為了與現(xiàn)實(shí)生活更加接近,本文首先對原有的Vasicek隨機(jī)利率模型進(jìn)行改進(jìn),將模型的系數(shù)改進(jìn)為與時(shí)間t有關(guān),并將單因子Vasicek隨機(jī)利率模型擴(kuò)展為多因子Vasicek隨機(jī)利率模型.接著應(yīng)用Ito引理求出貼現(xiàn)債券滿足的隨機(jī)微分方程.最后,我們應(yīng)用Girsanov定理及鞅定價(jià)理論推導(dǎo)出在模型的系數(shù)與時(shí)間t有關(guān)的多因子Vasicek隨即利率模型下,貼現(xiàn)債券上的期權(quán)定價(jià)公式以及在此模型下復(fù)合期權(quán)定價(jià)公式.
[Abstract]:Financial engineering is a systematic subject, which includes the design of financial products, the pricing of financial products, the trading strategies of financial products and the management of financial risks. How to price financial products is one of the most important issues. Financiers and mathematicians have done a lot of research to find reasonable pricing of financial products. Based on the previous research results, this paper studies the pricing of composite options on discounted bonds. Considering that the price fluctuation of discount bond is closely related to the fluctuation of interest rate, in order to be closer to the real life, this paper first improves the original Vasicek stochastic interest rate model, and improves the coefficient of the model to time t. The single-factor Vasicek stochastic interest rate model is extended to the multi-factor Vasicek stochastic interest rate model. Then the stochastic differential equations of discounted bonds are obtained by using Ito Lemma. Finally, we use Girsanov theorem and martingale pricing theory to deduce the option pricing formula on discounted bonds and compound option pricing formula under the multi-factor Vasicek random interest rate model in which the coefficient of the model is related to time t.
【學(xué)位授予單位】：河北師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F830.91;F224

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 李淑錦;李勝宏;;隨機(jī)利率下奇異期權(quán)的定價(jià)公式[J];數(shù)學(xué)學(xué)報(bào);2008年02期

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本文編號：1776466