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

10.6545/JFS.201809_26(3).0003

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)

American option ； binary power option ； early exercise premium ； 美式選擇權 ； 二元乘冪選擇權 ； 提早履約溢酬

財務金融學刊

26卷3期（2018 / 09 / 30）

91 - 116

英文

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).

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)。

1. Barone-Adesi, Giovanni,Whaley, Robert E.(1987).Efficient analytical approximation of American option values.Journal of Finance,42,301-320.
2. Broadie, Mark,Detemple, Jerome(1996).American option valuation: New bounds, approximations, and a comparison of existing methods.Review of Financial Studies,9,1211-1250.
3. Broadie, Mark,Detemple, Jerome(2004).Option pricing: Valuation models and applications.Management Science,50,1145-1177.
4. Broadie, Mark,Glasserman, Paul(1997).Pricing American-style securities using simulation.Journal of Economic Dynamics and Control,21,1323-1352.
5. Chung, San-Lin,Shih, Pai-Ta(2007).Generalized Cox-Ross-Rubinstein binomial models.Management Science,53,508-520.
6. Chung, San-Lin,Shih, Pai-Ta(2009).Static hedging and pricing American options.Journal of Banking and Finance,33,2140-2149.
7. Figlewski, Stephen,Gao, Bin(1999).The adaptive mesh model: A new approach to efficient option pricing.Journal of Financial Economics,53,313-351.
8. Geske, Robert,Johnson, Herb E.(1984).The American put option valued analytically.Journal of Finance,39,1511-1524.
9. Heston, Steve,Zhou, Guofu(2000).On the rate of convergence of discrete-time contingent claims.Mathematical Finance,10,53-75.
10. 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.
11. Ju, Nengjiu(1998).Pricing an American option by approximating its early exercise boundary as a piecewise exponential function.Review of Financial Studies,11,627-646.
12. Longstaff, Francis A.,Schwartz, Eduardo S.(2001).Valuing American options by simulations: A simple least-squares approach.Review of Financial Studies,14,113-147.
13. Macovschi, Stefan,Quittard-Pinon, François(2006).On the pricing of power and other polynomial options.Journal of Derivatives,13,61-72.
14. Medvedev, Alexey,Scaillet, Olivier(2010).Pricing American options under stochastic volatility and stochastic interest rates.Journal of Financial Еconomics,98,145-159.
15. Sullivan, Michael A.(2000).Valuing American put options using Gaussian quadrature.Review of Financial Studies,13,75-94.
16. Zhang, Jin E.,Li, Tiecheng(2010).Pricing and hedging American options analytically: A perturbation method.Mathematical Finance,20,59-87.

1. 黃明官,吳明遠(2019).Using the Expected Final Return Model to Create Optimal Trading Strategy for Options: A Theoretical and Empirical Study Based on Evidence from Short Combination Strategy.財務金融學刊,27(3),111-145.