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NTU Management Review
Vol. 34 No. 1 Apr. 2024, 1-44
https://doi.org/10.6226/NTUMR.202404_34(1).0001

Valuation of Spread and Basket Options

價差選擇權與一籃子選擇權之評價

Jui-Jane Chang, Department of Financial Engineering and Actuarial Mathematics, Soochow
University
張瑞珍 / 東吳大學財務工程與精算數學系
Pao-Hsien Huang, Department of Money and Banking, National Kaohsiung University of
Science and Technology
黃保憲 / 國立高雄科技大學金融系
Kun-Li Lin, Department of Business Management, National Taichung University of Science and
Technology
林昆立 / 國立臺中科技大學商業經營系
Ting-Pin Wu, Department of Finance, National Central University
吳庭斌 / 國立中央大學財務金融學系
Received 2021/7, Final revision received 2023/5
Abstract
This study adopts the unbounded-system distribution of the Johnson (1949) distribution
family to approximate the basket/spread distribution and derive a versatile pricing
model. This pricing model can price both basket and spread options, and thus, the risks
of issuing both options can be consistently and efficiently integrated and managed.
Furthermore, the pricing model can instantly price basket/spread options (almost as short
in time as the Black-Scholes model (Black and Scholes, 1973)), and the results are quite
accurate compared with the Monte Carlo simulation results. The method for computing
Greeks is also presented. Finally, numerical examples are provided to demonstrate the
implementation of the pricing model, and show the economic intuitions of Greeks for
basket and spread options, and for an option portfolio consisting of both options.
【Keywords】basket options, spread options, martingale pricing method

摘 要
本研究採用 Johnson (1949) 分配族中的無邊界系統分配來近似一籃子 / 價差標的資產
分配並推導出定價模型。該定價模型可以對一籃子選擇權和價差選擇權進行定價，因
此可以一致且有效地整合及管理發行這兩種選擇權的風險。又，該定價模型可以即時
對一籃子 / 價差選擇權進行定價（時間幾乎與 Black-Scholes (Black and Scholes, 1973)
評價模型一致），且與蒙地卡羅模擬的評價結果相比，顯示其定價結果相當準確。本
研究還介紹了計算 Greeks 的方法。最後，數值範例展示定價模型的實作結果，並呈
現一籃子選擇權、價差選擇權及兩種選擇權組成的選擇權組合等商品 Greeks 分別的
經濟直覺。

【關鍵字】 一籃子選擇權、價差選擇權、平賭過程評價方法

領域主編：王衍智教授

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