Uncertainty Estimates in the Heston Model via Fisher Information

TL;DR

This paper investigates how well European option prices inform about volatility in the Heston model using Fisher information, revealing conditions under which volatility estimates are reliable or impossible.

Contribution

It introduces a Fisher information-based approach to quantify the information content of option prices about volatility within the Heston model, highlighting the impact of volatility levels.

Findings

Reliable volatility estimates when volatility is high

Vega approaches zero at low volatility, impairing inference

Fisher information quantifies the limits of volatility estimation

Abstract

We address the information content of European option prices about volatility in terms of the Fisher information matrix. We assume that observed option prices are centred on the theoretical price provided by Heston's model disturbed by additive Gaussian noise. We fit the likelihood function on the components of the VIX, i.e., near- and next-term put and call options on the S&P 500 with more than 23 days and less than 37 days to expiration and non-vanishing bid, and compute their Fisher information matrices from the Greeks in the Heston model. We find that option prices allow reliable estimates of volatility with negligible uncertainty as long as volatility is large enough. Interestingly, if volatility drops below a critical value, inferences from option prices become impossible because Vega, the derivative of a European option w.r.t. volatility, nearly vanishes.