本文選題：已實(shí)現(xiàn)波動(dòng)率 + 多分形波動(dòng)率　； 參考：《浙江工商大學(xué)》2017年碩士論文

【摘要】：隨著我國金融市場的發(fā)展,市場對(duì)金融衍生品的定價(jià)需求也越來越迫切,然而常用的經(jīng)典B-S定價(jià)模型假定波動(dòng)率為固定不變的常數(shù),這顯然不符合金融市場的實(shí)際情況。在以往的研究中,很多學(xué)者曾使用GARCH族模型來估計(jì)股票的波動(dòng)率,然而,近年來針對(duì)我國金融市場的研究發(fā)現(xiàn),金融市場具有多重分形性,即長記憶性。為了在B-S模型中反映我國市場的這一特性,本文將引入新的多分形波動(dòng)率測度方法(MVM),并建立能夠刻畫時(shí)間序列長記憶性的ARFIMA模型,分析不同多分形波動(dòng)率測度方法及其動(dòng)力學(xué)模型對(duì)金融衍生品定價(jià)的影響。本文選取寶鋼權(quán)證存續(xù)期間標(biāo)的股票的5分鐘高頻數(shù)據(jù)作為研究樣本,首先對(duì)樣本區(qū)間內(nèi)寶鋼股票的收盤價(jià)、日收益率序列和已實(shí)現(xiàn)波動(dòng)率序列的統(tǒng)計(jì)特征進(jìn)行研究。研究結(jié)果發(fā)現(xiàn)樣本的日收益率序列和已實(shí)現(xiàn)波動(dòng)率序列均不服從正態(tài)分布,而是具有更為復(fù)雜的多重分形特征。為了能夠建立準(zhǔn)確的波動(dòng)率預(yù)測模型,并結(jié)合序列的多分形特征,本文引入利用已實(shí)現(xiàn)波動(dòng)率和多分形譜標(biāo)準(zhǔn)差作為修正參數(shù)計(jì)算基準(zhǔn)的新的多分形波動(dòng)率測度方法(MVM),并基于已實(shí)現(xiàn)波動(dòng)率和新舊多分形波動(dòng)率序列分別建立短記憶的ARMA模型(ARMA-LnRV、ARMA-LnMVM 等)和具有長記憶性的 ARFIMA模型(ARFIMA-LnRV、ARFIMA-LnMVM等)對(duì)股票收益未來10的波動(dòng)率進(jìn)行預(yù)測。最后,將上文不同模型預(yù)測得到的波動(dòng)率作為真實(shí)波動(dòng)率的代理變量分別代入B-S模型中,計(jì)算檢驗(yàn)樣本區(qū)間內(nèi)權(quán)證的理論價(jià)格。并比較未來10天權(quán)證的理論價(jià)格和市場價(jià)格之間的差異,根據(jù)理論價(jià)格和市場價(jià)格的相對(duì)誤差判斷不同波動(dòng)率預(yù)測模型對(duì)B-S模型定價(jià)精度的影響,最終發(fā)現(xiàn)新的多分形波動(dòng)率測度方法及其動(dòng)力學(xué)模型(ARFIMA-LnMVM)的預(yù)測效果是最優(yōu)的。將利用該模型預(yù)測得到的波動(dòng)率代入分形B-S模型中計(jì)算得到的權(quán)證價(jià)格更接近權(quán)證的市場價(jià)格。
[Abstract]:With the development of financial market in China, the demand for financial derivatives pricing is becoming more and more urgent. However, the classical B-S pricing model assumes that volatility is a constant constant, which obviously does not accord with the actual situation of financial market. In previous studies, many scholars have used the GARCH family model to estimate the volatility of stocks. However, in recent years, research on financial markets in China has found that financial markets have multifractal, that is, long memory. In order to reflect this characteristic of Chinese market in B-S model, a new multifractal volatility measurement method is introduced in this paper, and a ARFIMA model which can describe the long memory property of time series is established. The effects of different multifractal volatility measurement methods and their dynamic models on the pricing of financial derivatives are analyzed. In this paper, five minute high frequency data of the underlying stock in Baosteel warrant period is selected as the research sample. Firstly, the statistical characteristics of the closing price, the daily yield series and the realized volatility series of Baosteel stock in the sample interval are studied. It is found that both the daily rate of return series and the realized volatility series of samples are not subject to normal distribution, but have more complex multifractal characteristics. In order to establish an accurate volatility prediction model and combine the multifractal features of the series, In this paper, a new multifractal volatility measurement method based on realized volatility and multifractal spectral standard deviation is introduced. Based on realized volatility and new and old multifractal volatility series, a new multifractal volatility measurement method is introduced. The ARFIMA-LnRVV ARFIMA-LnMVM) and the long-memory ARFIMA model ARFIMA-LnRVMVM) are used to predict the volatility of stock returns in the next 10 years. Finally, the volatility predicted by different models above is substituted into B-S model as the proxy variable of real volatility, and the theoretical price of warrants in the test sample interval is calculated. The difference between the theoretical price and the market price of warrants in the next 10 days is compared, and the influence of different volatility forecasting models on the pricing accuracy of B-S model is judged according to the relative error between theoretical price and market price. Finally, it is found that the new multifractal volatility measurement method and its dynamic model ARFIMA-LnMVMM are the best. The volatility predicted by this model is substituted in the fractal B-S model to calculate the warrant price which is closer to the market price of warrant.
【學(xué)位授予單位】：浙江工商大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F832.51

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本文編號(hào)：1840967