A Study on the Initial Value Problem of Option Pricing Taking Double Reset Options as an Example

初始值問題於選擇權評價之研究－以雙重重設選擇權為例

蕭義龍(Yi-Long Hsiao)

《中國統計學報》 50卷4期 (2012/12) Pp. 242-268

https://doi.org/10.29973/JCSA.201212.0004

摘要

本研究使用格林函數之回溯積分表現法來探討初始值問題於選擇權之評價－以雙重重設選擇權為例，針對積分公式使用複合式辛普森法，可獲得近似理論收斂等級4之高收斂性數值解析解，並以數值例來探討雙重重設選擇權之相關性質。本研究提出之方法可進一步應用於具有複雜結構之初始值相關評價問題，例如提供公司在複合條件下員工選擇權決策之有效參考依據。

關鍵字

格林函數 ； 回溯積分表現法 ； 雙重重設選擇權

並列摘要

Herein, we discuss the valuation of the initial value problem using a recursive integral representation with Green's function, and we take the double reset call pricing as an example. When we use the composite Simpson's Rule for the integration, we obtain the numerical analytic solution with a high convergent numerical order 4. We provide some numerical examples to discuss the properties of the double reset option and find some characteristics of the option. Our method can apply to evaluations of relative initial-value contracts with more complex term structures and provide an effective reference for the policy decisions regarding the design of executive stock warrants in corporate finance.

並列關鍵字

Green's function ； recursive integral representation ； double reset options