本文關(guān)鍵詞：美式期權(quán)最優(yōu)實(shí)施邊界的單調(diào)迭代算法及其在定價(jià)計(jì)算中的應(yīng)用　出處：《華東師范大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 美式看跌期權(quán) 最優(yōu)實(shí)施邊界 單調(diào)迭代算法 數(shù)值定價(jià) 上下解

【摘要】：美式看跌期權(quán)的最優(yōu)實(shí)施邊界滿足一個(gè)非線性第二類Volterra積分方程.對(duì)這樣的積分方程給出有效的數(shù)值算法具有一定的實(shí)際意義.本文利用復(fù)合梯形公式將該積分方程離散成為一個(gè)非線性函數(shù)方程組.利用上下解方法,證明了非線性函數(shù)方程組解的存在唯一性,并建立了一種求解的單調(diào)迭代算法.當(dāng)初始迭代是一對(duì)耦合的上下解時(shí),迭代序列單調(diào)遞減或遞增收斂于方程組的唯一解.另外,本文也系統(tǒng)地給出了構(gòu)造耦合上下解的一個(gè)算法.作為上述算法的應(yīng)用,本文將上述算法與美式看跌期權(quán)的分解定理相結(jié)合,給出了一種美式期權(quán)的數(shù)值定價(jià)算法.對(duì)美式期權(quán)定價(jià)進(jìn)行了數(shù)值模擬,數(shù)值結(jié)果顯示了算法的有效性和穩(wěn)定性.
[Abstract]:The optimal implementation of the American option boundary satisfies a nonlinear Volterra integral equation of the second kind. It has certain practical significance for efficient numerical algorithm of integral equation given this. In this paper, using the composite trapezoidal formula to discrete the integral equation into a nonlinear equations. By using the method of upper and lower solutions, we prove the existence and uniqueness of solution the nonlinear equations, and the establishment of a monotone iterative algorithm for solving. When the initial iteration is a coupling of the upper and lower solutions, iterative sequence of monotone decreasing or recursive solution only increase convergence in equations. In addition, this paper also systematically gives an algorithm to construct the coupling of upper and lower solutions as. Based on the above algorithm, the decomposition theorem of the algorithm and the American option combination gives the numerical algorithm for pricing American options. For American option pricing are calculated numerically. The numerical results show the effectiveness and stability of the algorithm.

【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：O241.8;F830.9

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 張鐵;美式期權(quán)定價(jià)問(wèn)題的數(shù)值方法[J];應(yīng)用數(shù)學(xué)學(xué)報(bào);2002年01期

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本文編號(hào)：1373154