question: public static double blackFormulaStdDevDerivative ( @ Real double strike , @ Real double forward , @ StdDev final double stddev , @ DiscountFactor final double discount , @ Real final double displacement ) { QL . require ( strike >= 0.0 , "strike must be non-negative" ) ; QL . require ( forward > 0.0 , "forward must be positive" ) ; QL . require ( stddev >= 0.0 , "blackPrice must be non-negative" ) ; QL . require ( discount > 0.0 , "discount must be positive" ) ; QL . require ( displacement >= 0.0 , "displacement must be non-negative" ) ; forward = forward + displacement ; strike = strike + displacement ; final double d1 = Math . log ( forward / strike ) / stddev + .5 * stddev ; final CumulativeNormalDistribution cdf = new CumulativeNormalDistribution ( ) ; return discount * forward * cdf . derivative ( d1 ) ; }
target:  Black 1976 formula for standard deviation derivative <p>