## Interface SabrVolatilityFormula

• All Known Implementing Classes:
SabrHaganNormalVolatilityFormula, SabrHaganVolatilityFunctionProvider

public interface SabrVolatilityFormula
Provides volatility and sensitivity in the SABR model.
• ### Method Summary

All Methods
Modifier and Type Method Description
ValueType getVolatilityType()
static SabrVolatilityFormula hagan()
The Hagan SABR volatility formula.
double volatility​(double forward, double strike, double timeToExpiry, double alpha, double beta, double rho, double nu)
Calculates the volatility.
ValueDerivatives volatilityAdjoint​(double forward, double strike, double timeToExpiry, double alpha, double beta, double rho, double nu)
Calculates volatility and the adjoint (volatility sensitivity to forward, strike and model parameters).
• ### Method Detail

• #### hagan

static SabrVolatilityFormula hagan()
The Hagan SABR volatility formula.

This provides the functions of volatility and its sensitivity to the SABR model parameters based on the original Hagan SABR formula.

Reference: Hagan, P.; Kumar, D.; Lesniewski, A. & Woodward, D. "Managing smile risk", Wilmott Magazine, 2002, September, 84-108

OpenGamma documentation: SABR Implementation, OpenGamma documentation n. 33, April 2016.

Returns:
the SABR Hagan formula
• #### volatility

double volatility​(double forward,
double strike,
double timeToExpiry,
double alpha,
double beta,
double rho,
double nu)
Calculates the volatility.
Parameters:
forward - the forward value of the underlying
strike - the strike value of the option
timeToExpiry - the time to expiry of the option
alpha - the SABR alpha value
beta - the SABR beta value
rho - the SABR rho value
nu - the SABR nu value
Returns:
the volatility

ValueDerivatives volatilityAdjoint​(double forward,
double strike,
double timeToExpiry,
double alpha,
double beta,
double rho,
double nu)
Calculates volatility and the adjoint (volatility sensitivity to forward, strike and model parameters).

By default the derivatives are computed by central finite difference approximation. This should be overridden in each subclass.

Parameters:
forward - the forward value of the underlying
strike - the strike value of the option
timeToExpiry - the time to expiry of the option
alpha - the SABR alpha value
beta - the SABR beta value
rho - the SABR rho value
nu - the SABR nu value
Returns:
the volatility and associated derivatives