Estimating Option Pricing Models Using a Characteristic Function-Based Linear State Space Representation

TL;DR

This paper introduces a new filtering and estimation method for affine jump-diffusion option pricing models using characteristic functions, enabling efficient parameter estimation and state inference.

Contribution

It develops a linear state space representation based on characteristic functions and applies a modified Kalman filter for parameter and state estimation in complex models.

Findings

Effective in Monte Carlo simulations for finite-sample performance.

Successfully applied to S&P 500 options and Covid-19 related economic variables.

Provides computational advantages over traditional methods.

Abstract

We develop a novel filtering and estimation procedure for parametric option pricing models driven by general affine jump-diffusions. Our procedure is based on the comparison between an option-implied, model-free representation of the conditional log-characteristic function and the model-implied conditional log-characteristic function, which is functionally affine in the model's state vector. We formally derive an associated linear state space representation and establish the asymptotic properties of the corresponding measurement errors. The state space representation allows us to use a suitably modified Kalman filtering technique to learn about the latent state vector and a quasi-maximum likelihood estimator of the model parameters, which brings important computational advantages. We analyze the finite-sample behavior of our procedure in Monte Carlo simulations. The applicability of our procedure is illustrated in two case studies that analyze S&P 500 option prices and the impact of exogenous state variables capturing Covid-19 reproduction and economic policy uncertainty.