A Simple Iterative Method for the Valuation of American Options

Forthcoming, Quantitative Finance

Posted: 28 Apr 2006 Last revised: 22 May 2012

See all articles by In Joon Kim

In Joon Kim

Yonsei University - School of Business

Bong-Gyu Jang

Pohang University of Science and Technology (POSTECH)

Kyeong Tae Kim

POSTECH

Date Written: January 15, 2012

Abstract

We introduce a simple iterative method to determine the optimal exercise boundary for American options, allowing us to compute the values of American options and their Greeks quickly and accurately. Following Little, Pant, and Hou’s (2000) idea, we derive a new equation for the optimal exercise boundary containing a single integral. The proposed method is an iterative numerical method for finding its solution. Using it, we can calculate the entire optimal exercise boundary in a non-time-recursive way, while conventional methods do not. Extensive numerical results indicate that our method is computationally more efficient than the methods currently available, particularly when finding hedge ratios.

Keywords: American option, iteration, exercise boundary, early exercise premium, numerical method

JEL Classification: C63, G13

Suggested Citation

Kim, In Joon and Jang, Bong-Gyu and Kim, Kyeong Tae, A Simple Iterative Method for the Valuation of American Options (January 15, 2012). Forthcoming, Quantitative Finance. Available at SSRN: https://ssrn.com/abstract=898781 or http://dx.doi.org/10.2139/ssrn.898781

In Joon Kim

Yonsei University - School of Business ( email )

Seoul
Korea, Republic of (South Korea)
822-2123-5489 (Phone)
822-364-7828 (Fax)

Bong-Gyu Jang (Contact Author)

Pohang University of Science and Technology (POSTECH) ( email )

77 Cheongam-ro
Pohang
Korea, Republic of (South Korea)

Kyeong Tae Kim

POSTECH ( email )

Nam-gu, Hyoja-dong
Pohang, Kyung-Buk
Korea

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