Approximate arbitrage-free option pricing under the SABR model

Nian Yang, Nan Chen, Yanchu Liu and Xiangwei Wan

Journal of Economic Dynamics and Control, 2017, vol. 83, issue C, 198-214

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 (search for similar items in EconPapers)
JEL-codes: C63 G13 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016518891730177X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:83:y:2017:i:c:p:198-214

DOI: 10.1016/j.jedc.2017.08.004

Access Statistics for this article

Journal of Economic Dynamics and Control is currently edited by J. Bullard, C. Chiarella, H. Dawid, C. H. Hommes, P. Klein and C. Otrok

More articles in Journal of Economic Dynamics and Control from Elsevier
Bibliographic data for series maintained by Catherine Liu ().