Stress Testing Option Sensitivities in a Stochastic Market

ABSTRACT

The Heston stochastic volatility model aims to parameterise the equity market with 5 specific parameters. It is arguably one of the most popular models used in option pricing, since it relaxes the Black–Scholes assumption of constant volatility, and can capture the observed equity skew. Another reason for its popularity is the fact that it has an analytical solution for European options and associated option sensitivities called the Greeks. In this paper, we analyse the sensitivity of the three main option sensitivities Delta, Gamma, and Vega, to changes in market conditions. We specifically test what happens to each option sensitivity in a bear market—as we currently face in the wake of COVID-19. We find that the option sensitivities are linked to the Heston model parameters;therefore, the Heston model parameters should give market makers an idea of future option behaviour. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.