# Bayesian Approach for Parameter Estimation of Continuous-Time Stochastic Volatility Models using Fourier Transform Methods

## TL;DR

This paper introduces a Bayesian method utilizing Fourier transform-based volatility estimation to infer parameters of continuous-time stochastic volatility models, demonstrating high accuracy for Heston models but limited success for more complex models.

## Contribution

It develops a novel two-stage Bayesian estimation procedure combining Fourier-based volatility estimation with prior-informed likelihood construction.

## Key findings

- Highly effective for Heston model parameter estimation
- Limited success with exponential-Ornstein-Uhlenbeck model
- Demonstrates the utility of Fourier methods in Bayesian inference

## Abstract

We propose a two stage procedure for the estimation of the parameters of a fairly general, continuous-time stochastic volatility. An important ingredient of the proposed method is the Cuchiero-Teichmann volatility estimator, which is based on Fourier transforms and provides a continuous time estimate of the latent process. This estimate is then used to construct an approximate likelihood for the parameters of interest, whose restrictions are taken into account through prior distributions. The procedure is shown to be highly successful for constructing the posterior distribution of the parameters of a Heston model, while limited success is achieved when applied to the highly parametrized exponential-Ornstein-Uhlenbeck.