Analytic Calibration in Andreasen-Huge SABR Model

TL;DR

This paper derives analytic formulas linking key parameters of the Andreasen-Huge SABR model to observable option prices, enabling better calibration and understanding of the model's behavior.

Contribution

It introduces explicit analytic formulae connecting SABR parameters to option prices and their derivatives, improving calibration methods for interest rate derivatives.

Findings

Analytic formulas accurately relate SABR parameters to ATM and near-ATM option prices.

The approach enables effective calibration of the SABR model to market data.

Application to interest rate futures options demonstrates practical utility.

Abstract

We derive analytic formulae which link $\alpha$, $\nu$ and $\rho$ parameters in Andreasen-Huge style SABR model to the ATM price and option prices at four strikes close to ATM. Based on these formulae we give a characterisation for the SABR parameters in terms of derivatives of the swap rate forward probability density function. We test the analytic result in the application to the interest rate futures option market.