本文選題：亞式期權(quán) + 自融資交易策略��； 參考：《中國礦業(yè)大學(xué)》2017年碩士論文

【摘要】：亞式期權(quán)是一種強(qiáng)路徑依賴型奇異期權(quán),它在到期日的收益依賴于標(biāo)的資產(chǎn)價格在整個有效期內(nèi)的平均值,從而減少了價格的波動,使得亞式期權(quán)比常規(guī)期權(quán)更受歡迎。目前對亞式期權(quán)定價問題的研究大多是建立在標(biāo)準(zhǔn)布朗運(yùn)動上,并且假設(shè)標(biāo)的資產(chǎn)價格是連續(xù)不斷的,同時不需要支付交易費(fèi)用。但標(biāo)的資產(chǎn)價格呈現(xiàn)出一種“尖峰厚尾”的分布,且存在自相似性和長期相關(guān)性;加上實際金融市場存在大量的交易費(fèi)用,因此本文將在分?jǐn)?shù)跳-擴(kuò)散和混合分?jǐn)?shù)跳-擴(kuò)散兩種模型下研究帶比例交易費(fèi)的亞式期權(quán)定價問題。主要內(nèi)容如下:(1)應(yīng)用分?jǐn)?shù)?Ito公式推導(dǎo)出混合分?jǐn)?shù)跳-擴(kuò)散過程的?Ito公式,并采用自融資交易策略得到亞式期權(quán)的定價模型,通過求解定價模型得到亞式看漲期權(quán)以及看跌期權(quán)的價值。最后,運(yùn)用Matlab軟件進(jìn)行數(shù)值實驗,討論定價參數(shù)赫斯特指數(shù)、跳躍強(qiáng)度、股票價格等對期權(quán)價值的影響。(2)利用分?jǐn)?shù)跳-擴(kuò)散過程下的?Ito公式和自融資交易策略建立帶交易費(fèi)用的亞式期權(quán)定價模型,通過定義Leland數(shù)來簡化波動率修正因子,從而簡化定價模型,再運(yùn)用變量替換的方法對模型進(jìn)行求解,得到期權(quán)價值的解析解。數(shù)值實驗直觀的反映了期權(quán)價值與赫斯特指數(shù)、跳躍強(qiáng)度以及交易費(fèi)率等的關(guān)系。(3)建立了混合分?jǐn)?shù)跳-擴(kuò)散過程下帶交易費(fèi)的亞式期權(quán)定價模型,通過降維的方法將三維問題轉(zhuǎn)化為二維熱傳導(dǎo)方程,并通過對經(jīng)典熱傳導(dǎo)方程的求解得到亞式看漲期權(quán)的定價公式,從而推導(dǎo)出看跌期權(quán)的定價公式。數(shù)值實驗探究了赫斯特指數(shù)、交易費(fèi)率、無風(fēng)險利率以及股票價格等對期權(quán)價值的影響,并得出在一定程度上混合分?jǐn)?shù)跳-擴(kuò)散模型更貼近實際金融市場,比分?jǐn)?shù)跳-擴(kuò)散模型具有更好的穩(wěn)定性。
[Abstract]:Asian option is a kind of strong path dependent singular option. Its return on maturity date depends on the average value of the underlying asset price in the whole period of validity, which reduces the fluctuation of price and makes the Asian option more popular than the conventional option. At present, most of the researches on Asian option pricing are based on the standard Brownian motion, and assume that the underlying asset price is continuous and the transaction cost is not required. But the underlying asset price shows a "peak and thick tail" distribution, and there is self-similarity and long-term correlation. In addition, there are a lot of transaction costs in the actual financial markets. In this paper, we will study the pricing of Asian options with proportional transaction costs in two models: fractional hopping diffusion and mixed fractional hopping diffusion. The main contents are as follows: (1) the mixed fractional hop-diffusion process is derived by using the fractional Ito formula, and the pricing model of Asian options is obtained by using the self-financing trading strategy. The value of Asian call option and put option is obtained by solving pricing model. Finally, using Matlab software to carry on the numerical experiment, discuss the pricing parameter Hurst index, jump intensity, The influence of stock price on the value of options. (2) by using the Fractional Leap-Diffusion formula and self-financing trading strategy, the Asian option pricing model with transaction costs is established, and the volatility correction factor is simplified by defining the Leland number. Then the pricing model is simplified and the model is solved by the method of variable substitution, and the analytical solution of option value is obtained. Numerical experiments directly reflect the relationship between option value and Hurst index, jump intensity and transaction rate, etc.) A pricing model of Asian option with transaction cost under mixed fractional hopping and diffusion process is established. The three-dimensional problem is transformed into two-dimensional heat conduction equation by dimensionality reduction method. By solving the classical heat conduction equation, the pricing formula of Asian call option is obtained, and the pricing formula of put option is deduced. The effects of Hurst index, transaction rate, risk-free interest rate and stock price on the value of options are explored, and the mixed fractional jump-diffusion model is found to be closer to the real financial market to a certain extent. It has better stability than fractional hopping diffusion model.
【學(xué)位授予單位】：中國礦業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F830.91

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