價差選擇權與一籃子選擇權之評價

Valuation of Spread and Basket Options

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。

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.