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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bakshi, G., Cao, C., & Chen., Z. (1997). Empirical performance of alternative option pricing models. Journal of Finance, 52(5), 2033–49.
Bakshi, G., & Madan, D. (2000). Spanning and derivative-security valuation. Journal of Financial Economics, 55, 205–38.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.
Cox, J., Ingersoll, J., & Ross, S. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385–407.
Heston, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies, 6(2), 327–343.
Hull, J. (2012). Options, futures and other derivatives (8th ed.). Upper Saddle River: Prentice Hall.
Rouah, F. (2013). The Heston model and its extensions in Matlab and C#. Hoboken: Wiley.
Zhu, J. (2010). Applications of Fourier transform to smile modeling: Theory and implementation (2nd ed.). New York, NY: Springer.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Levendis, A., Venter, P., Maré, E. (2021). Stress Testing Option Sensitivities in a Stochastic Market. In: Tsounis, N., Vlachvei, A. (eds) Advances in Longitudinal Data Methods in Applied Economic Research. ICOAE 2020. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-63970-9_30
Download citation
DOI: https://doi.org/10.1007/978-3-030-63970-9_30
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-63969-3
Online ISBN: 978-3-030-63970-9
eBook Packages: Economics and FinanceEconomics and Finance (R0)