本文選題：亞式期權(quán) + 回望期權(quán)�。� 參考：《西南財(cái)經(jīng)大學(xué)》2012年碩士論文

【摘要】：強(qiáng)路徑有關(guān)期權(quán)在期權(quán)到期日的收益不僅依賴于當(dāng)天標(biāo)的資產(chǎn)的價(jià)格,而且依賴于在整個(gè)(或部分)有效期內(nèi)期權(quán)標(biāo)的資產(chǎn)價(jià)格歷程。主要有依賴于價(jià)格的平均值的亞式期權(quán)和依賴于價(jià)格最大(小)值的回望期權(quán)。由于亞式期權(quán)具有強(qiáng)路徑依賴性,所以其風(fēng)險(xiǎn)要小于標(biāo)準(zhǔn)期權(quán),那么,價(jià)格也要低于標(biāo)準(zhǔn)期權(quán)。同樣回望期權(quán)的收益對(duì)標(biāo)的資產(chǎn)在期權(quán)有效期內(nèi)價(jià)格演化的依賴也非常強(qiáng),這類期權(quán)的收益高,相應(yīng)的價(jià)格十分昂貴。由于這類期權(quán)的強(qiáng)路徑依賴性,其定價(jià)問(wèn)題也變得相當(dāng)復(fù)雜。 在以前的期權(quán)定價(jià)問(wèn)題研究中,通常假定利率為常數(shù),這樣就可以使得問(wèn)題變得相對(duì)較為簡(jiǎn)單。然而,在期權(quán)定價(jià)問(wèn)題中市場(chǎng)是不穩(wěn)定的,即便是短期利率也是不斷發(fā)生變化的。那么,通常在期權(quán)定價(jià)時(shí)利率在期權(quán)有效期內(nèi)不變這一假定,就不能夠滿足實(shí)際運(yùn)用中的需要。因此,在研究期權(quán)定價(jià)時(shí)就可以考慮加入利率不確定性這一因素。 本文在CIR隨機(jī)利率模型下,建立了具有浮動(dòng)敲定價(jià)格亞式期權(quán)以及回望期權(quán)的定價(jià)模型；同時(shí),在考慮期權(quán)定價(jià)問(wèn)題時(shí)加入了標(biāo)的股票資產(chǎn)支付紅利以及可提前執(zhí)行這兩種因素。并利用有限差分法給出了相應(yīng)模型的數(shù)值解。最后分別給出實(shí)例,利用MATLAB編程求出其數(shù)值解。本文所提出的CIR隨機(jī)利率模型下亞式期權(quán)和回望期權(quán)定價(jià)模型更符合實(shí)際。
[Abstract]:The yield of the option on the maturity of the option depends not only on the price of the underlying asset on that day, but also on the price process of the underlying asset during the whole (or part) period of validity of the option. There are mainly Asian options which depend on the average value of the price and the lookback options which depend on the maximum (small) value of the price. Because Asian option has strong path dependence, its risk is smaller than standard option, so the price is lower than standard option. The return of the option is also very dependent on the price evolution of the underlying asset during the period of validity of the option. The return of this kind of option is high and the corresponding price is very expensive. Because of the strong path dependence of this kind of option, the pricing problem becomes quite complicated. In previous studies of option pricing, the interest rate is usually assumed to be constant, which makes the problem relatively simple. However, the market is unstable in options pricing, and even short-term interest rates are constantly changing. Therefore, the assumption that the interest rate will not change during the term of the option when the option is priced can not meet the needs of practical application. Therefore, interest rate uncertainty can be taken into account when studying option pricing. In this paper, under the CIR stochastic interest rate model, we establish the pricing model of Asian option with floating strike price and the option of looking back, and at the same time, When considering option pricing, two factors are added: dividend payment of underlying stock assets and early execution. The numerical solution of the model is given by the finite difference method. Finally, examples are given and the numerical solution is obtained by MATLAB programming. In this paper, the pricing model of Asian option and lookback option under CIR stochastic interest rate model is more practical.
【學(xué)位授予單位】：西南財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：F830.9;F224

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本文編號(hào)：1949338