本文關(guān)鍵詞： VIX-已實現(xiàn)GARCH 模型期權(quán)定價 隱含波動率　出處：《吉林大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：現(xiàn)代期權(quán)定價理論有兩個發(fā)展方向,一個以模型為基礎(chǔ),通過建立無套利等價組合,推導(dǎo)微分方程,隨后尋求方程的解析解或者數(shù)值解;另一個是從歷史信息出發(fā),挖掘歷史價格信息,通過預(yù)測對期權(quán)價格有決定性影響的因子的未來值來確定未來期權(quán)價格。盡管目前模型法求解期權(quán)價值的研究已經(jīng)進(jìn)入較為深入的階段,取得了較為豐富的成果,但是由于多數(shù)模型應(yīng)用難度大,該方法遇到了普及困難的問題。而通過非模型方法為期權(quán)定價,正逐漸得到更多的關(guān)注。首先本文對要研究問題的選題背景和意義進(jìn)行了闡述,對傳統(tǒng)模型定價方法進(jìn)行了梳理,介紹了非模型期權(quán)定價基本方法。其次,本文梳理了單元GARCH和多元GARCH模型設(shè)定和估計方法,并說明了GARCH模型在期權(quán)定價中的應(yīng)用。本文在以往學(xué)者研究的基礎(chǔ)上,對隱含波動率和實際波動率動態(tài)對沖關(guān)系進(jìn)行建模,并結(jié)合正則期權(quán)定價模型來為期權(quán)進(jìn)行定價。已實現(xiàn)方法差的加入能顯著提高GARCH模型擬合和預(yù)測資產(chǎn)波動率的能力。本文借鑒這個思路,在GARCH模型基礎(chǔ)上加入了已實現(xiàn)協(xié)方差,建立了VIX-已實現(xiàn)GARCH模型,試圖提高模型的預(yù)測能力。本文采用兩階段擬極大似然估計方法對建立的已實現(xiàn)單元和多元GARCH模型參數(shù)進(jìn)行估計,在第一階段股價波動率方程中使用了已實現(xiàn)GARCH模型,這樣建立了VIX-收益率-已實現(xiàn)方差模型。使用標(biāo)準(zhǔn)普爾500指數(shù),芝加哥交易所發(fā)布隱含波動率VIX指數(shù),標(biāo)準(zhǔn)普爾500期權(quán),對提出已實現(xiàn)DCC-GARCH模型期權(quán)定價能力進(jìn)行了檢測。選用2000年1月3日到2016年12月21日作為樣本,本文分別將使用VIX-已實現(xiàn)GARCH模型來估計的波動率和使用普通GARCH模型估計的波動率代入到正則期權(quán)定價模型中去,通過對比誤差項,來比較兩者定價的效率。最終的研究結(jié)果顯示:隱含波動率指數(shù)和標(biāo)準(zhǔn)普爾500指數(shù)收益率具有明顯的負(fù)相關(guān)性,隱含波動率意味著未來收益率的降低;高頻已實現(xiàn)協(xié)方差對低頻隱含波動率和實際方差之間相關(guān)性具有顯著的影響,在模型中添加已實現(xiàn)協(xié)方差是必要的;本文提出的已實現(xiàn)DCC模型可以對未來隱含波動率做出良好的預(yù)測,但是仍有系統(tǒng)性低估未來隱含波動率的可能;基于本文提出的已實現(xiàn)DCC-GARCH模型的正則期權(quán)定價模型比基于普通GARCH模型的正則期權(quán)定價模型更優(yōu)越。
[Abstract]:Modern option pricing theory has two development directions, one is based on model, by establishing equivalent combination of no arbitrage, deducing differential equation, and then seeking analytic solution or numerical solution of equation, the other is based on historical information. Mining historical price information and predicting the future value of the factors that have a decisive effect on the option price are used to determine the future option price, although the study of solving the option value by the current model method has entered a deeper stage. But because most models are difficult to apply, it is difficult to popularize the method. First of all, this paper expounds the background and significance of the topics to be studied, combs the traditional model pricing methods, and introduces the basic pricing methods of non-model options. This paper reviews the methods of setting and estimating unit GARCH and multivariate GARCH models, and explains the application of GARCH model in option pricing. Based on the previous researches, this paper models the dynamic hedging relationship between implied volatility and actual volatility. The ability of GARCH model to fit and predict the volatility of assets can be significantly improved by adding the difference in the realized methods. This paper uses this idea for reference and adds realized covariance to the GARCH model. The VIX- implemented GARCH model is established to improve the prediction ability of the model. In this paper, the parameters of the implemented unit and the multivariate GARCH model are estimated by using the two-stage quasi-maximum likelihood estimation method. The realized GARCH model is used in the first stage of the stock price volatility equation, thus the VIX- yield realized variance model is established. Using the Standard & Poor's 500 Index, the Chicago Exchange issues the implied volatility VIX Index, the Standard & Poor's 500 option. The option pricing ability of the proposed DCC-GARCH model is tested. The sample is from January 3rd 2000 to December 21st 2016. In this paper, the volatility estimated by using VIX- implemented GARCH model and the volatility estimated by ordinary GARCH model are substituted into the regular option pricing model, and the error terms are compared. Finally, the results show that the yield of implied volatility index and S & P 500 index have obvious negative correlation, and implied volatility rate means the decline of future rate of return; The high frequency realized covariance has a significant influence on the correlation between the low frequency implied volatility and the actual variance, so it is necessary to add the realized covariance to the model. The realized DCC model proposed in this paper can make a good prediction of the future implied volatility, but it is still possible to systematically underestimate the future implied volatility. The regular option pricing model based on the realized DCC-GARCH model is superior to the regular option pricing model based on the ordinary GARCH model.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F830.9

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本文編號：1517179