Option Pricing Accuracy for Estimated Heston Models

TL;DR

This paper develops a method to quantify how estimation errors in Heston model parameters affect option pricing, using PDEs and applying it to real market data for the S&P 500 and VIX.

Contribution

It introduces a novel approach combining PDE solutions and parameter error estimation to assess option pricing inaccuracies in Heston models.

Findings

Quantifies option pricing errors due to parameter estimation.

Provides a practical framework applied to S&P 500 and VIX data.

Analyzes sensitivity to market price of volatility risk.

Abstract

We consider assets for which price $X_t$ and squared volatility $Y_t$ are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from $N$ sub-sampled data $(X_{nT}, Y_{nT})$, estimation errors do impact the classical option pricing PDEs. We estimate these option pricing errors by combining numerical evaluation of estimation errors for Heston SDEs parameters with the computation of option price partial derivatives with respect to these SDEs parameters. This is achieved by solving six parabolic PDEs with adequate boundary conditions. To implement this approach, we also develop an estimator $\hat \lambda$ for the market price of volatility risk, and we study the sensitivity of option pricing to estimation errors affecting $\hat \lambda$. We illustrate this approach by fitting Heston SDEs to 252 daily joint observations of the S\&P 500 index and of its approximate volatility VIX, and by numerical applications to European options written on the S\&P 500 index.