What is the SABR Hagan implied vol formula?

sigma_B(K,F) = alpha / (F*K)^((1-beta)/2) * (1 + (1-beta)^2/24 * ln^2(F/K) + ...) * (1 + ((1-beta)^2/24 * alpha^2 + rho*beta*nu*alpha/4 + (2-3*rho^2)/24*nu^2)*T).

What does beta control in SABR?

Beta controls the backbone: beta=0 gives normal SABR (log-normal vol), beta=1 gives log-normal SABR. Typically beta=0.5 is fixed and only alpha, nu, rho are calibrated.

SABR Model Alpha Nu Rho Calibration Calculator

Calibrate SABR stochastic alpha-beta-rho model parameters to market smile. Hagan approximation gives closed-form implied vol as function of strike, enabling fast calibration.

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$ Finance Disclaimer: These calculators are for educational and illustrative purposes only. Results do not constitute financial advice. Consult a licensed financial advisor before making investment or borrowing decisions.

How to Use

Enter the values for the scenario you are assessing. Calibrate SABR stochastic alpha-beta-rho model parameters to market smile. Hagan approximation gives closed-form implied vol as function of strike, enabling fast calibration. Use the sabr calibration result to inform your calculation.

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SABR Model Alpha Nu Rho Calibration Calculator

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Frequently Asked Questions

What is the SABR Hagan implied vol formula?

What does beta control in SABR?