On Practitioners Closed-Form GARCH Option Pricing

Abstract

This paper proposes a practitioner version of Heston and Nandi's (2000) (HN) model, which we term the Practitioner's Heston Nandi, or PHN model. We compare the option pricing and hedging performance of the PHN model vis-à-vis the HN model. Instead of using a one-period ahead volatility forecast for all options used in calibrations at any given time, the PHN model proposes using forward-looking ad-hoc volatilities (implied by market option prices) for each individual option and maturity in calibration and hedging. Since the proposed PHN model uses only option price data, it renders historical stock price data redundant, cutting the data requirement in derivative valuation. We employ options traded at CBOE for the period January 1, 2016 to December 31, 2018 and show that the proposed PHN model yields quick calibration and significantly improves pricing and hedging for European-style options.