The SABR model is widely used by practitioners in the financial industry, especially in the interest rates derivatives markets. A suitable characteristic of any local and stochastic volatility model is that the model can yield the same prices of the vanilla options that were applied as inputs to the calibration of the model. failure to do so will clearly cause the model not arbitrage free and generate it nearly useless.
The SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for “Stochastic Alpha, Beta, Rho”, referring to the parameters of the model.
A substantial point of the SABR model is that the prices of vanilla options can be computed in almost closed form (Subject to the precise of a series expansion). Basically it has been shown that the price of a vanilla option under the SABR model is yielded by the suitable Black model, given that the correct implied volatility is employed.
Recently the SABR model has been developed to manage the option smile which is observed in derivatives markets. Typically, calibration of such models is straightforward as there is adequate data available for robust extraction of the parameters required asinputs to the model. The paper considers calibration of the model in situations where input data is very sparse. Although this will require some creative decision making, the algorithms developed here are remarkably robust and can be used confidently for mark to market and hedging of option portfolios.