FX Volatility Smile Construction

danielyng · January 5th, 2010, 9:50 pm

Did anyone read the above captioned paper by Reiswich and Wystup?I like it. However, I could not reproduce the numerical result. Base on the data from table 4 in the paper, the USDJPY forward price is 90.686. Since USDJPY is premium adjusted, Atm strike is 90.516 using the formula f exp(-0.5 sigma^2 tau). However, the atm strike for USDJPY is 90.86 in table 5. Do I miss anything?

Leonidas · January 8th, 2010, 6:49 pm

The ATM quotation is not considered as premium adjusted in this case but as the simple delta neutral forwarddelta quotation. So with f exp(+0.5 sigma^2 tau) you should be fine