The SABR Model

This quantitative finance training course is on the SABR (Stochastic Alpha Beta Rho) model, one popular stochastic volatility model developed to model the dynamic of the forward price and to price options.

It assumes that its variance alpha is stochastic as well and that the forward price and its variance are correlated.

There is no closed-form solution for the pricing of vanilla options under the SABR model except when the parameter beta is equal to zero or one but there is a good asymptotic estimation.

With its four parameters, the model allows to reproduce a large number of volatility curves. We will discuss on how the different parameters of the model impact the implied volatility curve.

We will see how to estimate the risk-neutral density function in the SABR model using the Breeden-Litzenberger formula and how the different parameters impact the moments of the return distribution.

We will see as well how to calibrate model parameters to market prices, discussing on how to improve the stability of the parameters.

We will compare the estimation of the true value of vanilla option prices under the SABR model by Monte Carlo simulations with the asymptotic estimate for different sets of parameters.

We will see how to price and risk manage exotic option payoffs with the SABR model, analysing the sensitivity of option prices when changing SABR parameters.

We will finally discuss the limits of the model.

The course is composed of many videos, quizzes, applications in Python.

A certificate of achievements will be delivered once the course has been completed with success.