Approximate Arbitrage-Free Option Pricing Under the SABR Model

22 Pages Posted: 20 Oct 2016 Last revised: 13 Sep 2017

See all articles by Nian Yang

Nian Yang

Nanjing University - School of Business

Nan Chen

The Chinese University of Hong Kong (CUHK)

Yanchu Liu

Lingnan (University) College, Sun Yat-sen University, Guangzhou, China.

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management

Date Written: October 19, 2016

Abstract

The stochastic-alpha-beta-rho (SABR) model introduced by Hagan et al. (2002) provides a popular vehicle to model the implied volatilities in the interest rate and foreign exchange markets. To exclude arbitrage opportunities, we need to specify an absorbing boundary at zero for this model, which the existing analytical approaches to pricing derivatives under the SABR model typically ignore. This paper develops closed-form approximations to the prices of vanilla options to incorporate the effect of such a boundary condition. Different from the traditional normal distribution-based approximations, our method stems from an expansion around a one-dimensional Bessel process. Extensive numerical experiments demonstrate its accuracy and efficiency. Furthermore, the explicit expression yielded from our method is appealing from the practical perspective because it can lead to fast calibration, pricing, and hedging.

Keywords: SABR model; Approximate solution; Arbitrage-free option pricing; Perturbation method

JEL Classification: C63; G13

Suggested Citation

Yang, Nian and Chen, Nan and Liu, Yanchu and Wan, Xiangwei, Approximate Arbitrage-Free Option Pricing Under the SABR Model (October 19, 2016). Journal of Economic Dynamics and Control, Vol. 83, 2017, Available at SSRN: https://ssrn.com/abstract=2854797 or http://dx.doi.org/10.2139/ssrn.2854797

Nian Yang (Contact Author)

Nanjing University - School of Business ( email )

Nanjing
China

Nan Chen

The Chinese University of Hong Kong (CUHK) ( email )

Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://www.se.cuhk.edu.hk/people/nchen.html

Yanchu Liu

Lingnan (University) College, Sun Yat-sen University, Guangzhou, China. ( email )

Haizhu District,
Guangzhou, China.
Guangzhou, Guangdong 510275
China

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management ( email )

No.1954 Huashan Road
Shanghai Jiao Tong University
Shanghai, Shanghai 200030
China
+86-21-52301570 (Phone)

HOME PAGE: http://sites.google.com/view/wanxiangwei/research

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