Fitting the implied volatility surface

In the context of exotic derivatives, arbitrage-free implied volatility surfaces are a crucial ingredient to sophisticated pricing routines. We use a non-linear optimization technique to fit an arbitrage-free implied volatility surface efficiently to market data. The fitting procedure is tailor-made for any analytic parametrization of the single volatility skews. We carry out this approach for a certain parametrization by implementing an Interior-Point method, discuss its shortcomings, potentials, as well as specific smoothing techniques. Besides all the theory, we give various fitting details and examples by using real market data.

Autorentext

Immanuel Dobler was born and raised in Southern Germany. After graduating from High School in 2008, he successfully and ambitiously completed his Bachelor's and Master's degree in Mathematical Economics at Ulm University. Since 2014, he has been working for the Risk Methodology Department of Landesbank Baden-Württemberg (LBBW) in Stuttgart.