## Archive for **June 2011**

## SABR model calibration

**Don’t use this!**

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 :

## Is EUR/USD mean reverting?

Nassim Taleb in his book “Dynamic Hedging” provides an empirical rule to validate if the market has mean reversion tendency. It states that if volatility lowers if the longer time frame is used, then the mean reversion takes place.

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## Exponential Ornstein-Uhlenbeck process

Let’s consider parameter estimation for the following modification of Ornstein-Uhlenbeck process:

This model is simplification of Schwarz Model 1, one of Short-rate models

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