本文選題：交易費用 + 離散型　； 參考：《華中師范大學(xué)》2013年碩士論文

【摘要】：為了滿足金融市場發(fā)展的需要,二十世紀(jì)九十年代,亞式期權(quán)作為一種新型期權(quán)(路徑依賴的期權(quán))首次在日本東京問世。亞式期權(quán)有三大優(yōu)點：(1)能有效防止人為操縱標(biāo)的資產(chǎn)的價格,維護市場公平性；(2)對于套期保值者而言,產(chǎn)生的金融風(fēng)險相對較��；(3)相比標(biāo)準(zhǔn)的歐式期權(quán),其自身的價格也比較便宜。因此,亞式期權(quán)的優(yōu)勢更加明顯,它已逐漸成為市場關(guān)注的焦點,其定價問題也成為人們研究的熱點。亞式期權(quán)主要有兩種類型：一是幾何平均亞式期權(quán),二是算術(shù)平均亞式期權(quán)。對于前者而言,其標(biāo)的資產(chǎn)價格的幾何平均值仍滿足對數(shù)正態(tài)分布,因此可用經(jīng)典的方法為其求解,但對于后者而言,其標(biāo)的資產(chǎn)價格的算術(shù)平均值卻不滿足對數(shù)正態(tài)分布,通常采用近似的方法為算術(shù)平均亞式期權(quán)定價。 本文研究算術(shù)平均亞式期權(quán)的定價問題,并對有交易費用的離散型算術(shù)平均亞式期權(quán)的定價問題進行了深入探討,分為到期日較短和較長兩種情形。對于到期日較短的情形采用的是蒙特卡洛的數(shù)值方法,而對于到期日比較長的情形則采用如下的近似定價方法,即先把期權(quán)有效期內(nèi)某個時間段[t,T]均分成M-1個時間段,并計算這M個時間點上的期望收益,然后求和取平均,比較此平均值與有交易費用的離散型算術(shù)平均亞式期權(quán)的期望收益之間的漸進關(guān)系,得到一個近似解,從而為有交易費用的離散型算術(shù)平均亞式期權(quán)進行近似定價,最后,本文給出了一個相關(guān)的數(shù)值例子。
[Abstract]:In order to meet the needs of the development of financial market, Asian option, as a new type of option (path dependent option), was first introduced in Tokyo, Japan in the 1990s.Asian option has three major advantages: 1) it can effectively prevent artificial manipulation of the price of the underlying asset and maintain market fairness. For hedgers, the financial risk generated is relatively small) compared with the standard European option.Its own price is also relatively cheap.Therefore, the advantage of Asian option is more obvious, it has gradually become the focus of market attention, and its pricing has become a hot topic.There are two main types of Asian options: one is geometric average Asian option, the other is arithmetic average Asian option.For the former, the geometric average value of the underlying asset price still satisfies the logarithmic normal distribution, so it can be solved by the classical method, but for the latter, the arithmetic average of the underlying asset price does not satisfy the logarithmic normal distribution.An approximate method is usually used to price the arithmetic average Asian option.In this paper, the pricing problem of arithmetic average Asian option is studied, and the pricing problem of discrete arithmetic average Asian option with transaction costs is discussed in depth, which can be divided into two cases: shorter maturity date and longer maturity date.In the case of shorter maturity date, Monte Carlo numerical method is used, while in the case of long maturity date, the approximate pricing method is used, that is to say, [t T] is divided into M-1 time periods in a certain period of validity of an option.The expected income at M time points is calculated, then the sum is averaged, and the asymptotic relationship between the mean value and the expected return of discrete arithmetic average Asian option with transaction costs is compared, and an approximate solution is obtained.In order to approximate the pricing of discrete arithmetic average Asian options with transaction costs, a numerical example is given in this paper.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F224;F830.9

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本文編號：1765606