Looking at the papers
- Arbitrage free SABR (Hagan)
- Managing Smile Risk (Hagan)
- Explicit SABR Calibration through simple expansions (Floch)
all 3 papers have similar forms for expression for implied volaility (Normal) but differ quite a little. But that is not my main question.
When F = K, the implied normal volaility breaks down when i tried to implement them, either divide by 0 or 0/0.
Can i get some help on this?