Calibration and Filtering of Exponential L\'evy Option Pricing Models

TL;DR

This paper compares calibration techniques for exponential Lévy models in option pricing, focusing on least squares and particle filtering, and investigates their convergence to consistent parameters.

Contribution

It introduces a unified framework for calibrating exponential Lévy models using regularized least squares and particle filtering, analyzing their convergence and consistency.

Findings

Calibration methods converge to the same parameters.

Algorithms effectively find global optima.

Parallelizable statistical optimization enhances efficiency.

Abstract

The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential L\'evy processes are calibrated using regularized weighted least squares with respect to the minimal entropy martingale measure. Sequential importance resampling is used for the Bayesian inference problem of time series parameter estimation with proposal distribution determined using extended Kalman filter. The algorithms converge to their respective global optima using a highly parallelizable statistical optimization approach using a grid of initial positions. Each of these methods should produce the same parameters. We investigate this assertion.