The Survival Probability of the SABR Model: Asymptotics and Application
29 Pages Posted: 29 Oct 2016 Last revised: 9 Jan 2018
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: Suggested Citation