public static double volatilityConversionLognormalATMtoNormalATM ( double forward , double displacement , double maturity , double lognormalVolatiltiy ) { double x = lognormalVolatiltiy * Math . sqrt ( maturity / 8 ) ; double y = org . apache . commons . math3 . special . Erf . erf ( x ) ; double normalVol = Math . sqrt ( 2 * Math . PI / maturity ) * ( forward + displacement ) * y ; return normalVol ; }
Exact conversion of displaced lognormal ATM volatiltiy to normal ATM volatility .