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 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...

In this paper, by adopting a quasi-Lamperti transform unitizing the process’ diffusion matrix at the initial time, we provide a new explicit recursive formula to compute the expansion coefficients for the pathwise Taylor expansion method of Li (2013). The quasi-Lamperti transform also allows...

This paper shows that a small-time Hermite expansion is feasible for multivariate diffusions. By introducing an innovative quasi-Lamperti transform, which unitizes the diffusion matrix at the initial time, we derive explicit recursive formulas for the expansion coefficients of transition...