The survival probability of the SABR model: asymptotics and application
研究了SABR模型下远期价格不触及非负下边界的生存概率，给出了新的渐近公式和误差估计，对无套利隐含波动率和二元敲出期权定价有重要应用。
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 (see, e.g. De Marco et al. [SIAM J. Financ. Math., 2017, 8(1), 709–737], Gulisashvili [Int. J. Theor. Appl. Financ., 2015, 18, 1550013], Gulisashvili et al. [Mass at zero in the uncorrelated SABR modeland implied volatility asymptotics, 2016b]), 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.