Numerical Approximation of the Implied Volatility under Arithmetic Brownian Motion

8 Pages Posted: 4 Jun 2007 Last revised: 16 Nov 2016

See all articles by Jaehyuk Choi

Jaehyuk Choi

Peking University - HSBC School of Business

Kwangmoon Kim

Korea Advanced Institute of Science and Technology (KAIST)

Minsuk Kwak

Department of Mathematics, Hankuk University of Foreign Studies

Date Written: June 1, 2007

Abstract

We provide an accurate approximation method for inverting an option price to the implied volatility under arithmetic Brownian motion. The maximum error in the volatility is in the order of 1e-10 of the given option price and much smaller for the near-the-money options. Thus our approximation can be used as a near-exact solution without further refinements of iterative methods.

Keywords: implied volatility, arithmetic Brownian motion, ABM, Bachelier, rational approximation, closed form approximation

JEL Classification: C63, G12

Suggested Citation

Choi, Jaehyuk and Kim, Kwangmoon and Kwak, Minsuk, Numerical Approximation of the Implied Volatility under Arithmetic Brownian Motion (June 1, 2007). Applied Mathematical Finance, Vol. 16, No. 3, 2009. Available at SSRN: https://ssrn.com/abstract=990747 or http://dx.doi.org/10.2139/ssrn.990747

Jaehyuk Choi (Contact Author)

Peking University - HSBC School of Business ( email )

University Town
Shenzhen, Guangdong 518055
China

HOME PAGE: http://www.jaehyukchoi.net/phbs_en

Kwangmoon Kim

Korea Advanced Institute of Science and Technology (KAIST) ( email )

373-1 Kusong-dong
Yuson-gu
Taejon 305-701, 130-722
Korea, Republic of (South Korea)

Minsuk Kwak

Department of Mathematics, Hankuk University of Foreign Studies ( email )

81 Oedae-ro
Yongin, 449-791
Korea, Republic of (South Korea)

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