發(fā)布時(shí)間：2018-04-28 22:05

  本文選題：貝葉斯方法 + 期權(quán)定價(jià)�。� 參考：《湖南大學(xué)》2013年碩士論文

【摘要】：隨著金融衍生品市場(chǎng)的發(fā)展,金融衍生品交易的規(guī)模不斷擴(kuò)大,同時(shí)也出現(xiàn)了一些衍生品的定價(jià)方法.多年以來,有很多學(xué)者在經(jīng)典統(tǒng)計(jì)學(xué)的框架下對(duì)B-S模型進(jìn)行了研究,但是同時(shí)也存在著一些不足,模型當(dāng)中的資產(chǎn)價(jià)格以及波動(dòng)率的隨機(jī)性問題一直沒有得到較好的解決.考慮到貝葉斯統(tǒng)計(jì)所具有的諸多優(yōu)點(diǎn),本文在貝葉斯統(tǒng)計(jì)的框架下結(jié)合B-S模型對(duì)期權(quán)的價(jià)格進(jìn)行推斷.首先采用Fisher信息矩陣來確定無風(fēng)險(xiǎn)資產(chǎn)回報(bào)率和波動(dòng)率的無信息先驗(yàn),并且將資產(chǎn)價(jià)格和波動(dòng)率都看成是隨機(jī)變量,然后運(yùn)用無風(fēng)險(xiǎn)資產(chǎn)回報(bào)率和波動(dòng)率的無信息先驗(yàn)并結(jié)合適當(dāng)?shù)乃迫缓瘮?shù),得出歐式看漲期權(quán)的先驗(yàn)密度以及后驗(yàn)密度函數(shù)的表達(dá)式. 本文采用中國的歐式認(rèn)購權(quán)證“鞍鋼JTC1”的日收盤價(jià)格數(shù)據(jù)以及其標(biāo)的資產(chǎn)的日收盤價(jià)格數(shù)據(jù)進(jìn)一步進(jìn)行了實(shí)證研究.在計(jì)算方面,考慮到蒙特卡羅模擬方法(MC)整體的運(yùn)算較為有效,且適用于標(biāo)的資產(chǎn)的預(yù)期收益率和波動(dòng)率的函數(shù)形式比較復(fù)雜的情況,所以本文運(yùn)用蒙特卡羅算法(MC)來獲得期權(quán)價(jià)格的估計(jì)值以及其它的數(shù)值特征,例如均值、方差等等,并且根據(jù)計(jì)算所得到的結(jié)果進(jìn)行了分析,分析表明隨著時(shí)間的增大,期權(quán)價(jià)格密度函數(shù)的收斂性增強(qiáng).然后,將計(jì)算得出的理論價(jià)格與相應(yīng)的實(shí)際價(jià)格進(jìn)行比較.最后,為了衡量出權(quán)證的市場(chǎng)價(jià)格與理論價(jià)格的偏離程度,本文采用了偏離度進(jìn)行分析研究.實(shí)證的結(jié)果表明:當(dāng)時(shí)間接近于到期日的時(shí)侯,權(quán)證的實(shí)際價(jià)格與其理論價(jià)格趨于一致,偏離度逐漸趨近于零.由此可以看出:權(quán)證標(biāo)的股票的交易者與權(quán)證的交易者對(duì)標(biāo)的股票價(jià)格的預(yù)期逐漸趨于一致.
[Abstract]:With the development of financial derivatives market, the scale of financial derivatives trading is expanding, and some derivatives pricing methods have emerged. For many years, many scholars have studied the B-S model under the framework of classical statistics, but at the same time, there are some shortcomings, the problem of asset price and volatility randomness in the model has not been solved. Considering the many advantages of Bayesian statistics, this paper inferred the price of options under the framework of Bayesian statistics combined with B-S model. Firstly, the Fisher information matrix is used to determine the non-information prior to the return and volatility of risk-free assets, and the asset price and volatility are regarded as random variables. Then the prior density and posteriori density function of European call options are obtained by using the non-information priori of risk-free return on assets and volatility and the appropriate likelihood function. This paper makes a further empirical study on the daily closing price data of the European subscription warrant "Angang JTC1" and the daily closing price data of its underlying assets. In terms of calculation, considering that the Monte Carlo simulation method / MCMC) is more effective in overall operation and is applicable to the complex function forms of the expected return and volatility of the underlying asset, So this paper uses Monte Carlo algorithm to get the estimated value of option price and other numerical characteristics, such as mean value, variance and so on, and according to the results of the calculation, the analysis shows that with the increase of time, The convergence of the option price density function is enhanced. Then, the calculated theoretical price is compared with the corresponding actual price. Finally, in order to measure the deviation degree between the market price and the theoretical price, the deviation degree is analyzed. The empirical results show that when the time is close to the maturity date, the actual price of warrant tends to be consistent with its theoretical price, and the deviation gradually approaches zero. It can be seen that the traders of the underlying stocks and the traders of warrants tend to converge on the price of the underlying stocks.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F830.9;F224

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