彭栢堅臺灣大學:數學研究所張祐誠Chang, You-ChenYou-ChenChang2010-05-052018-06-282010-05-052018-06-282008U0001-0307200819044300http://ntur.lib.ntu.edu.tw//handle/246246/180537本篇論文主要是探討如何利用 IMEX 的方法為跳躍市場的選擇權定價。除了一階的方法之外，我們還會探討多階的 Runge-Kutta 方法。最後我們還會以數值的結果來探討利用 Runge-Kutta 方法的優勢所在。This paper mainly discusses how to use the IMEX method to price options on a market with jumps. In addition to the first order method, we will discuss the IMEX Runge-Kutta method which is a higher order scheme. Finally, we will use the numerical examples to discuss the advantage of the IMEX Runge-Kutta method.中文摘要 . . i 文摘要 . . i 一章 Introduction . . 1 二章 Jump diffusion model and European option . . 2 2.1 Some background knowledge . . 2 .2 PIDE for pricing European options in a market with jumps . . 4 .3 IMEX on PIDE . . 6 .4 FFT implementation . . 10 三章 Jump diffusion model and American option: he first algorithm . . 12 四章 Jump diffusion model and American option: MEX Runge-Kutta scheme . . 17 五章 Numerical comparison of the two algorithms . . 27 amp;#63851;考文獻 . . 31application/pdf298904 bytesapplication/pdfen-US有限插分方法含有跳躍的擴散過程隱式-顯式的方法無條件地穩定快速傅立葉轉換朗格-古塔的方法Finite difference methodJump diffusion processIMEX methodUnconditionally stableFast Fourier transformRunge-Kutta schemethesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/180537/1/ntu-97-R94221033-1.pdf