## Archive for **November 1st, 2011**

## SABR model calibration – attempt 2

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. It was developed by Patrick Hagan, Deep Kumar, Andrew Lesniewski, and Diana Woodward.

The SABR model describes a single forward F, such as a LIBOR forward rate, a forward swap rate, or a forward stock price. The volatility of the forward F is described by a parameter σ. SABR is a dynamic model in which both F and σ are represented by stochastic state variables whose time evolution is given by the following system of stochastic differential equations:

Constant parameters should satisfy the condition

Here, and are two correlated Wiener processes with correlation coefficient . For simplicity sake, we assume that , therefore, we put :

## Correlation trading on FX

Correlation trading is based on few simple ideas:

- Correlations are changing with time
- Correlations of pairs of 3 currencies are bounded by strict equation
- Correlation is bound in the interval

Therefore, one may try to “buy correlation” at -1 and to “sell it” at +1.