Valuation of the Option in a continuous time GARCH-Model
When it comes to the valuation of the Option, we general use the Black-Scholes model .while this model assumes the volatility is constant , so the value of the option is different from the actual value of the option. How to describe the future value of the volatility , is very important for us to value the option. So we use GARCH-Model to value the option, which assume the volatility exist the functional relationships between the time of t and t-1. Many researches show that the value of the option which is used by GARCH-Model is more accurate than use by Black-Scholes model.
In this paper , firstly I describe the theory of the valuation of Thesis is provided by UK thesis base the option ,and find the faults of the currently model ,such as the Black-Scholes model. Secondly I describe the features of the GARCH-Model, particularity the advantage of this model. Thirdly I will do some empirical analysis, and use the GARCH model and the Black-Scholes to value some options ,including European option and American option. Fourthly I will compare the results of these models ,and analyze the results http://elviscollections.com/ .
Empirical Analysis of the “Flight-To-Quality-Effect”
Flight-To-Quality-Effect is a stock market phenomenon occurring when investors sell what they perceive to be higher-risk investments and purchase safer investments, this is considered a sign of fear in the marketplace, as investors seek less risk in exchange for lower profits. Base on the currently researches, we research what touch off the Flight-To-Quality-Effect, such as features of the Macroeconomic and the financial market
SABR model: the features of the model and valuation of the option
The SABR model is a new model , which is used in the value of the finance produces. I firstly describe the features of the SABR model .Then I will use SABR model to describe and research the Black-Volatility, including the sensitive of the Black-Volatility to every model. I also describe the function of the Balck-Volatility in the model. At last I will use SABR model to value the option according to the Monte-Cario Simulat
文章翻譯如下:
第一個(gè)題目:
“Empirical Analysis of the “Flight-To-Quality-Effect” ”
說(shuō)明:Flight-To-Quality-Effect 是投資者在金融市場(chǎng)上的一種行為模型。投資者賣出那些風(fēng)險(xiǎn)程度被估計(jì)得很高的債券,然后緊接著將自己的資產(chǎn)以低風(fēng)險(xiǎn)的債券為內(nèi)容進(jìn)行重組。
投資者可以間接地根據(jù) Flight-To-Quality-Effect 將手中的債券的收益固定化。根據(jù)“金融市場(chǎng)行情劇烈向下震蕩情況可以觸發(fā)Flight-To-Quality-Effect ”的理論假說(shuō),F(xiàn)light-To-Quality-Effect 將增加高風(fēng)險(xiǎn)債券的價(jià)格地下跌,同時(shí)提高低風(fēng)險(xiǎn)債券的賬面收益,也就增加了市場(chǎng)對(duì)低風(fēng)險(xiǎn)債券需求。
在發(fā)生 Flight-To-Quality 行為的經(jīng)濟(jì)周期內(nèi),兩種收益的相關(guān)性為負(fù)。這和普通經(jīng)濟(jì)環(huán)境下的相關(guān)性正相反。換句話說(shuō),相關(guān)性結(jié)構(gòu)是不平衡的,在此極端情況下發(fā)生了負(fù)相關(guān)性。#p#分頁(yè)標(biāo)題#e#
在前人研究的基礎(chǔ)上,我們dissertation的重點(diǎn)是尋找,這種Flight-To-Quality 效應(yīng)的觸發(fā)點(diǎn)是什么。(能夠觸發(fā)Flight-To-Quality 效應(yīng)的宏觀經(jīng)濟(jì)特征和金融市場(chǎng)元素。)
基礎(chǔ)知識(shí):
高階金融統(tǒng)計(jì)知識(shí):time series 理論,Copulas 理論,最大似然估計(jì)理論(Maximum-Likelihood-Estimation )
金融統(tǒng)計(jì)軟件知識(shí):EViews, Matlab
第二個(gè)題目:
Valuation of the Option in a continuous time GARCH-Model
在80年代由Robert F. Engle 和 Tim Bollerslev 提出的 Garch 模型,對(duì)金融市場(chǎng)和整體經(jīng)濟(jì)數(shù)據(jù)的時(shí)間動(dòng)態(tài)波動(dòng)率進(jìn)行分析。分析是基于如下假說(shuō):“隨機(jī)模型誤差的方差和前一時(shí)間階段實(shí)際發(fā)生的隨機(jī) 誤差相關(guān)”,在此情況下,大誤差和小誤差各自歸類分組。(波動(dòng)率—收縮率)
Garch 模型在今天得到了極大的深化和發(fā)展。07年,發(fā)展出了該模型在連續(xù)時(shí)間(continuous time)情況下的運(yùn)用。
dissertation的目的是:將 continuous time 條件下的 Garch 模型作為一個(gè)金融市場(chǎng)模型的隨機(jī)驅(qū)動(dòng)因素來(lái)進(jìn)行運(yùn)用。該模型將以隨機(jī)波動(dòng)率和倒閉風(fēng)險(xiǎn)作為自己的主要標(biāo)志。這使得該模型正好成為傳統(tǒng)的 Black Scholes 模型的對(duì)立物,在 Black Scholes 模型下,波動(dòng)率是恒定的,而且沒(méi)有破產(chǎn)風(fēng)險(xiǎn)。
dissertation首先應(yīng)該突出理論上的問(wèn)題,然后再研究模型的性質(zhì),波動(dòng)率的風(fēng)險(xiǎn)溢價(jià)也適用于倒閉風(fēng)險(xiǎn)。然后使用該模型對(duì)一個(gè) Plain Vanilla 期權(quán)在 Monte-Carlo 模擬法下進(jìn)行估值。
基礎(chǔ)知識(shí):
時(shí)間連續(xù)的隨機(jī)金融市場(chǎng):估值量和量的轉(zhuǎn)換,Levy Process
Matlab 軟件知識(shí)。
第三個(gè)題目:
SABR 模型:模型性質(zhì)和期權(quán)估值
隨機(jī)Alpha, Beta, Rho 波動(dòng)率模型(SABR 模型),是一個(gè)相對(duì)新的金融市場(chǎng)模型。目前該模型將加強(qiáng)其在衍生金融產(chǎn)品估值方面的應(yīng)用。
該模型的強(qiáng)點(diǎn)是,將短期的 Call Option 和 Put Option 的市場(chǎng)價(jià)格聯(lián)系起來(lái)。相對(duì)而言,在該模型中,波動(dòng)率的長(zhǎng)期發(fā)展趨勢(shì)實(shí)質(zhì)上解釋了,是什么主導(dǎo)了長(zhǎng)期 Option 的價(jià)格趨近市場(chǎng)價(jià)格。市場(chǎng)行話就是:該模型具有市場(chǎng)校正作用。這使得外部 Option 被準(zhǔn)確估值。
對(duì)于應(yīng)用者而言,該模型就是模型變量和Black-Volatility。這就是說(shuō),在市場(chǎng)中,Option 的價(jià)格將被包含Black-Volatility的Black-Scholes 方程來(lái)闡述。交易者將根據(jù) Black Volatility 而不是市場(chǎng)價(jià)格來(lái)對(duì)Option 進(jìn)行叫價(jià)。在SABR模型中,Black-Volatility被看作SABR參數(shù)的應(yīng)用。
本dissertation的第一目的是,描述SABR模型和模型的性質(zhì),第二步是詳細(xì)使用SABR模型參數(shù)對(duì)Black-Volatility 進(jìn)行研究和描述,包括Black-Volatility對(duì)每個(gè)單一模型參數(shù)的敏感度和Black-Volatility在模型中發(fā)揮的作用的確切而詳細(xì)的描述。最后請(qǐng)使用SABR模型按照Monte-Carlo 模擬法對(duì)一個(gè)Option進(jìn)行估值。#p#分頁(yè)標(biāo)題#e#
時(shí)間連續(xù)的隨機(jī)金融市場(chǎng):估值量和量的轉(zhuǎn)換,軟件知識(shí)。Wiener ProcessThesis is provided by UK thesis base http://elviscollections.com/Matlab
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