價差選擇權在雙資產Merton與Kou的跳躍擴散模型下之評價

Pricing Spread Options under Bivariate Merton's and Kou's Jump-Diffusion Models

張恩慈(En-Tzu Chang)

指導教授 ： 呂育道

共同指導教授 ： 繆維中(Wei-Chung Miao)

國立臺灣大學/管理學院/財務金融學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101125

摘要

價差選擇權是標的為兩資產的價差的選擇權，投資人可以輕易地透過價差選擇權間接投資兩種資產，因此價差選擇權現今被廣泛應用，如利率、股票、原油及外匯市場等等。然而由於價差選擇權沒有封閉解，因此在訂價及計算希臘字母（Greeks）相對不易。並且過去文獻中多是假設資產服從幾何布朗運動，實證發現，有重大資訊宣布或極端事件發生時，資產價格會有較大的跳動，並且分配呈高峰厚尾形狀，用幾何布朗運動皆無法捕捉此特性，因此本文引用Merton和Kou的跳躍擴散模型，並延伸其隨機過程至雙資產，以針對價差選擇權訂價。除了模型的延伸，本文更是整理了過去被提出的價差選擇權近似方法及數值解，將其延伸至Merton和Kou的跳躍擴散模型下雙資產的評價，從計算精確度及效率比較，在不同模型下找到最適合的訂價引擎。

關鍵字

價差選擇權 ； 跳躍擴散模型 ； 二元厚尾分配 ； 傅立葉轉換 ； 近似解析解 ； 高斯求積 ； Merton's jump-diffusion model ； Kou's jump-diffusion Model

並列摘要

A spread option is an option written on the difference between two assets. Investors can invest in both assets or hedge through spread options thus spread options are widely applied in various markets like interest rate, stock, commodity and foreign exchange markets. However, pricing methods are still in developing and it is hard to price and calculate the Greeks since there are no closed-form solutions of spread options. Moreover, assets are assumed to follow geometric Brownian motion in most literatures in the past which are found to be unable to capture the leptokurtic feature and asymmetric fat-tailed distributions in empirical research. Therefore, in this thesis, we would review Merton's and Kou's jump-diffusion models and extend formulas to bivariate distribution. In spite of the extension of models, we also review analytical approximations and numerical integration methods and apply those methods to Merton's and Kou's jump-diffusion models. We compare all methods through accuracy and efficiency in order to find the most suitable pricing engine to price spread options under different models.

並列關鍵字

Spread option ； Jump-Diffusion model ； Bivariate asymmetric Laplace ； Double Exponential ； Fast Fourier Transform ； Analytical Approximation ； Gauss-Hermite Quadrature ； Merton's jump-diffusion model ； Kou's jump-diffusion model ； double exponential jump-duffusion model

參考文獻

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