混合型指數跳躍擴散模型下雙界限選擇權之定價

The pricing of double barrier options under a mixed-exponential jump diffusion model

林彥誠(Yen-Chen Lin)

指導教授 ： 白惠明

國立臺北大學/商學院/統計學系/碩士(2013年)

摘要

本研究主要討論的是在混合型指數跳躍過程下雙界限選擇權的定價。模型包含了連續面的布朗運動及離散面的混合型指數分配，而利用混合型指數分配的特性，可以弱收斂到任何分配，如常用的厚尾分配。
由於混合型指數跳躍過程可以解決 overshoot 及 undersoot 的問題，因此利用 Laplace transform 可以求得第一次跳出的時間與 overshoot 的聯合分配，進而利用 double Laplace transform 求得第一次跳出的時間與最終值的聯合分配。
最後由計算出來的 Laplace transform 應用至評價雙界限選擇權，搭配 two-side, two-dimensional Euler inversion algorithm 求得選擇權價格。

關鍵字

混合型指數跳躍過程 ； 雙界限選擇權 ； Laplace transform ； Euler inversion algorithm

並列摘要

This paper studies the prices of double barrier options under a mixed-exponential jump diffusion model, which consists of a continuous part driven by Borownian motion and a jump part with jump sizes having a mixed-exponential distribution.The mixed-exponential distribution can approximate any distribution in the sense of weak convergence, including various heavy-tailed distributions.
Because of the capability of handling overshoot and undershoot under mixed-exponential jump diffusion process, an explicit form of the Laplace transform of the joint distribution of the first passage time and overshoot is derived.Base on this result, we obtain the double Laplace transform of the joint distribution of the first passage time and the asset price at the expiration date.
Finally, we apply the two-side, two-dimensional Euler inversion algorithm to the Laplace transforms and hence the prices of the double barrier options are obtained.

並列關鍵字

mixed-exponential jump diffusion process ； double-barrier option ； Laplace transform ； Euler inversion algorithm

參考文獻

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