發(fā)布時(shí)間：2018-03-21 04:43

  本文選題：多資產(chǎn)期權(quán)定價(jià)模型　切入點(diǎn)：Black-Sholes方程　出處：《華北電力大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

【摘要】：多資產(chǎn)期權(quán)在現(xiàn)代金融交易市場中占有重要的地位,研究多資產(chǎn)期權(quán)定價(jià)模型的數(shù)值解法具有非常重要的理論意義和應(yīng)用價(jià)值。本學(xué)位論文研究多資產(chǎn)期權(quán)定價(jià)模型中的三種典型模型(雙幣種期權(quán)定價(jià)模型、雙幣種交換期權(quán)定價(jià)模型和一籃子期權(quán)定價(jià)模型)的數(shù)值新方法,利用改進(jìn)的加性算子分裂(Additional Operator Splitting, AOS)算法對三種模型分別構(gòu)造了AOS-加權(quán)隱格式、AOS-不對稱格式、AOS-三時(shí)間層格式、AOS-顯隱格式和AOS-隱顯格式,分析這些差分格式的穩(wěn)定性、收斂性和計(jì)算精度。 雙幣種期權(quán)定價(jià)模型的差分格式求解：當(dāng)加權(quán)系數(shù)取2/1時(shí),AOS-加權(quán)隱格式為二階格式；AOS-不對稱格式是一種快速的差分格式,比計(jì)算解析解節(jié)省近86%的計(jì)算時(shí)間；AoS-顯隱格式和AOS-隱顯格式是無條件穩(wěn)定和收斂的二階格式,其綜合性能優(yōu)于經(jīng)典的Crank-Nicolson格式。雙幣種交換期權(quán)定價(jià)模型和一籃子期權(quán)定價(jià)模型的AOS-顯隱格式及AOS-隱顯格式的計(jì)算綜合性能較好,具有實(shí)際應(yīng)用價(jià)值。 理論分析和數(shù)值試驗(yàn)表明,本文的AOS-差分?jǐn)?shù)值方法可以有效解決多資產(chǎn)期權(quán)定價(jià)問題。
[Abstract]:Multi-asset options play an important role in the modern financial market. It is of great theoretical significance and practical value to study the numerical solution of multi-asset option pricing model. This dissertation studies three typical models of multi-asset option pricing model (dual-currency option pricing model). A new numerical method for the pricing of dual-currency exchange options and a basket of options. Using the improved additive Operator spliting algorithm, the AOS-weighted implicit scheme and the AOS-3-time implicit scheme are constructed, respectively, and the stability of these difference schemes is analyzed. Convergence and accuracy. The difference scheme of dual-currency option pricing model: when the weighting coefficient is 2/1, the AOS-weighted implicit scheme is a second-order scheme and the AOS-asymmetric scheme is a fast difference scheme. AoS- explicit schemes and AOS- implicit schemes are unconditionally stable and convergent second-order schemes, which save nearly 86% of computing time compared with analytical solutions. Its comprehensive performance is superior to the classical Crank-Nicolson scheme. The AOS- implicit scheme and the AOS- implicit scheme of the dual-currency exchange option pricing model and the basket option pricing model have good comprehensive performance and have practical application value. Theoretical analysis and numerical experiments show that the AOS- difference numerical method can effectively solve the multi-asset option pricing problem.
【學(xué)位授予單位】：華北電力大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F830.9;F224;O241.82

【參考文獻(xiàn)】

相關(guān)期刊論文 前4條

1 鄭小迎,陳金賢;有交易成本的期權(quán)定價(jià)方法[J];系統(tǒng)工程;2000年05期

2 唐耀宗;金朝嵩;;有紅利美式看跌期權(quán)定價(jià)的Crank-Nicolson有限差分法[J];經(jīng)濟(jì)數(shù)學(xué);2006年04期

3 李亞瓊;黃立宏;;兩種匯率制度的雙幣種期權(quán)定價(jià)模型及其解[J];經(jīng)濟(jì)數(shù)學(xué);2009年04期

4 劉棠,張盤銘;期權(quán)定價(jià)問題的數(shù)值方法[J];系統(tǒng)科學(xué)與數(shù)學(xué);2004年01期

，

本文編號：1642313