Levenberg-Marquat algorithm and Bayesian inference for SABR implied volatility smile parameter estimation

Francisco Pedro Furtado Simões

Key information

Authors:

Francisco Pedro Furtado Simões (Francisco Pedro Furtado Simões)

Supervisors:

Igor Kravchencko; Cláudia Rita Ribeiro Coelho Nunes Philippart (Cláudia Rita Ribeiro Coelho Nunes Philippart)

Published in

10/27/2020

Abstract

Under the hypothesis of the underlying asset of an option following the SABR model, we tested the Levenberg-Marquardt algorithm for volatility smile interpolation using the price of European options. This prove to be fast in the simulated framework. However, the real framework sometimes implies uneven distribution of quotes (with respect to relative strikes) or the presence of outliers, these two factors affect significantly the performance of the paremeter estimation using this algorithm. In this work it was also used Bayesian inference as an alternative to mitigate these limitations. We employed this approach on SABR's α parameter with good results.