Analytical Approximations for American Options: The Binary Power Option Approach

美式選擇權之解析近似：二元乘冪選擇權法

江彌修(Mi-Hsiu Chiang) ； 傅信豪(Hsin-Hao Fu) ； 黃以達(Yi-Ta Huang) ； 駱建陵(Chien-Ling Lo) ； 石百達(Pai-Ta Shih)

《財務金融學刊》 26卷3期 (2018/09) Pp. 91-116

https://doi.org/10.6545/JFS.201809_26(3).0003

摘要

This study proposes an innovative approach to value American options. Using a portfolio of binary power options to replicate the early exercise premium, we modify Medvedev and Scaillet (2010) to derive an analytical approximation of American option values under the Black-Scholes framework. Compared with Medvedev and Scaillet (2010), our approach provides a much simpler functional form of the early exercise premium that can be easily extended to high-order series expansions. The numerical results show that the pricing performance of our method is closely comparable to that of Medvedev and Scaillet (2010) and superior to that of Barone-Adesi and Whaley (1987).

關鍵字

American option ； binary power option ； early exercise premium

並列摘要

本研究提出一創新方法評價美式選擇權。利用二元乘冪選擇權之投資組合複製提早履約溢酬，本文在Black-Scholes架構下修改Medvedev and Scaillet (2010)方法，導出美式選擇權價格之解析近似。相較於Medvedev and Scaillet (2010)，本研究提供更為簡易之函數型式，並易於應用至高階級數。結果發現，本文方法堪比Medvedev and Scaillet (2010)所呈現之結果，並優於Barone-Adesi and Whaley (1987)。

並列關鍵字

美式選擇權 ； 二元乘冪選擇權 ； 提早履約溢酬

參考文獻

Chung, San-Lin, and Pai-Ta Shih, 2007, Generalized Cox-Ross-Rubinstein binomial models, Management Science 53, 508-520.

Chung, San-Lin, and Pai-Ta Shih, 2009, Static hedging and pricing American options, Journal of Banking and Finance 33, 2140-2149.

Figlewski, Stephen, and Bin Gao, 1999, The adaptive mesh model: A new approach to efficient option pricing, Journal of Financial Economics 53, 313-351.

Geske, Robert, and Herb E. Johnson, 1984, The American put option valued analytically, Journal of Finance 39, 1511-1524.

Heston, Steven L., 1993, A closed form solution for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies, 6, 327-343.