The Survival Probability of the SABR Model: Asymptotics and Application

29 Pages Posted: 29 Oct 2016 Last revised: 9 Jan 2018

See all articles by Nian Yang

Nian Yang

Nanjing University - School of Business

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management

Date Written: December 22, 2017

Abstract

The stochastic-alpha-beta-rho (SABR) model is widely used by practitioners in interest rate and foreign exchange markets. The probability of hitting zero sheds light on the arbitrage-free small strike implied volatility of the SABR model, and the survival probability is also closely related to binary knock-out options. Besides, the study of the survival probability is mathematically challenging. This paper provides novel asymptotic formulas for the survival probability of the SABR model as well as error estimates. The formulas give the probability that the forward price does not hit a nonnegative lower boundary before a fixed time horizon.

Keywords: SABR model; Survival probability; Probability of hitting zero; Implied volatility

JEL Classification: C63, G13

Suggested Citation

Yang, Nian and Wan, Xiangwei, The Survival Probability of the SABR Model: Asymptotics and Application (December 22, 2017). Available at SSRN: https://ssrn.com/abstract=2847553 or http://dx.doi.org/10.2139/ssrn.2847553

Nian Yang (Contact Author)

Nanjing University - School of Business ( email )

Nanjing
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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