本文關(guān)鍵詞：外匯期權(quán)定價問題的研究　出處：《燕山大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 外匯市場 外匯期權(quán) 匯率 期權(quán)定價模型 正態(tài)跳擴(kuò)散模型 二叉樹模型 保險(xiǎn)精算法 風(fēng)險(xiǎn)中性定價

【摘要】：在1973年Black和Scholes提出了Black-Scholes期權(quán)定價模型。把Black-Scholes定價模型應(yīng)用于外匯期權(quán)時即熟知的—G-K模型。著名Black-Scholes期權(quán)公式在金融衍生工具定價研究領(lǐng)域占有非常重要的位置，然而Black-Scholes期權(quán)公式在實(shí)際應(yīng)用中存在缺陷，主要是股價回報(bào)率的波動率假設(shè)為常數(shù)。而實(shí)際數(shù)據(jù)表明，股價回報(bào)率分布呈現(xiàn)兩個顯著特點(diǎn)：尖峰和厚尾，不符合標(biāo)準(zhǔn)正態(tài)分布的特征。因此人們開始研究更適合實(shí)際市場的股價行為模型，基于此，本文做了如下工作： 首先，對于經(jīng)典的外匯期權(quán)模型—G-K模型，采用了隨機(jī)微分方程法和保險(xiǎn)精算法兩種方法進(jìn)行了證明。對于隨機(jī)微分方程法，先求出外匯期權(quán)V所要滿足的偏微分方程，對該偏微分方程在有效期內(nèi)求定解問題，再進(jìn)行變換，然后應(yīng)用一般情況下的Black—Scholes期權(quán)定價模型就可證明出結(jié)果。對于保險(xiǎn)精算方法，利用期權(quán)在有效期內(nèi)所承擔(dān)風(fēng)險(xiǎn)的保障費(fèi)即所求期權(quán)的價格的原理，以二叉樹模型為基準(zhǔn)，結(jié)合外匯期權(quán)的特點(diǎn)，根據(jù)無套利原則和風(fēng)險(xiǎn)中性原則，推導(dǎo)出外匯期權(quán)的二叉樹模型。 其次，分析了外匯期權(quán)的二叉樹模型和G-K模型之間存在的聯(lián)系，利用風(fēng)險(xiǎn)中性原則法、中心極限定理以及二項(xiàng)式與二叉樹模型的相關(guān)性質(zhì)，在選擇適當(dāng)?shù)纳蠞q因子和下跌因子及上漲概率時，可用二叉樹模型逼近經(jīng)典外匯期權(quán)定價模型，并證明出了這個聯(lián)系。 最后，在前人研究的基礎(chǔ)上對G-K模型做了一些調(diào)整，建立了正態(tài)跳擴(kuò)散模型并將其應(yīng)用于外匯期權(quán)的定價。在外匯模型假設(shè)和正態(tài)跳擴(kuò)散模型的假設(shè)下，利用在一般均衡市場理論下的概率測度推導(dǎo)出了正態(tài)跳擴(kuò)散模型的外匯期權(quán)定價模型。還給出了此模型下的期貨期權(quán)的定價模型公式，，并證明了結(jié)論。
[Abstract]:In 1973, Black and Scholes put forward the Black-Scholes option pricing model. Black-Scholes pricing model was applied to foreign exchange options. Known -G-K model. The famous Black-Scholes option formula plays a very important role in the field of financial derivatives pricing. However, the Black-Scholes option formula has some defects in practical application, mainly because the volatility of the return on stock price is assumed to be constant. The distribution of return on stock price presents two remarkable characteristics: peak and thick tail, which do not accord with the characteristics of standard normal distribution. Therefore, people begin to study the stock price behavior model which is more suitable for the actual market. This paper has done the following work: First of all, for the classical foreign exchange options model-G-K model, the stochastic differential equation method and the actuarial insurance method are used to prove. For the stochastic differential equation method. The partial differential equation of foreign exchange option V is obtained first, and then the solution of the partial differential equation is obtained within the validity period, and then the transformation is carried out. Then the Black-Scholes option pricing model can be used to prove the result. Using the principle of the guarantee cost of the risk that the option bears during the period of validity, taking the binary tree model as the benchmark, combining the characteristics of the foreign exchange option, according to the principle of no arbitrage and risk neutrality. The binary tree model of foreign exchange options is derived. Secondly, the relationship between binomial tree model and G-K model of foreign exchange option is analyzed. The risk neutral principle, the central limit theorem and the properties of binomial and binomial tree model are used. When we select the appropriate rising factor, falling factor and rising probability, we can approach the classical foreign exchange option pricing model by using the binary tree model, and prove this connection. Finally, the G-K model is adjusted on the basis of previous studies, and the normal jump diffusion model is established and applied to the pricing of foreign exchange options, under the assumption of the foreign exchange model and the normal jump diffusion model. By using the probability measure under the general equilibrium market theory, the foreign exchange option pricing model of normal jump diffusion model is derived, the formula of futures option pricing model under this model is given, and the conclusion is proved.
【學(xué)位授予單位】：燕山大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F830.9;F224

【引證文獻(xiàn)】

相關(guān)期刊論文 前1條

1 羅斌;;外匯期權(quán)交易投資理財(cái)風(fēng)險(xiǎn)及盈利分析[J];中小企業(yè)管理與科技(下旬刊);2015年08期

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