Negative Rate and the Left Wing of Volatility Smile under SABR Process

The weakness of SABR model, proposed by Hagan, Kumar, Lesniewski and Woodward (2002), came to light in low and negative rate environment. The breakdown of Hagan's expansion can be explained by probability mass of forward... [ view full abstract ]

The weakness of SABR model, proposed by Hagan, Kumar, Lesniewski and Woodward (2002), came to light in low and negative rate environment. The breakdown of Hagan's expansion can be explained by probability mass of forward rate equals zero. My study investigates the asymptotic formula of implied volatility introduced in De Marco, Hillairet and Jacquire (2013) by considering mass at zero.  In my paper, the Fourier-cosine series expansion is used for computing mass at zero. The numerical results show that accuracy of asymptotic formula introduced by De Marco et al. (2013) is high.