Article: The sensitivity of variance risk premium estimates to grid and strike fineness: simulating the Heston model with jumps Journal: International Journal of Financial Markets and Derivatives (IJFMD) 2026 Vol.10 No.5 pp.1 - 17 Abstract: We investigate variance risk premiums in the Heston stochastic volatility model with Merton jumps. Risk neutral variance estimates are derived from out-of-the-money option-based integrands. In a controlled simulation setting with model-generated option prices and evenly spaced strikes, our results suggest that 12 or fewer option strikes are sufficient to obtain accurate model-free variance estimates - a finding with practical relevance for researchers working with illiquid underlyings where the available strike grid may be sparse. We find that sample variance is a better estimate of integrated variance than finite quadratic variation under a coarse grid. Model free methods give better estimates than averaged Black-Scholes implied volatilities. Inderscience Publishers - linking academia, business and industry through research

Title: The sensitivity of variance risk premium estimates to grid and strike fineness: simulating the Heston model with jumps

Authors: Jimmy E. Hilliard; Jitka Hilliard; Yufei Wu

Addresses: Department of Finance, Raymond J. Harbert College of Business, Auburn University, Auburn, Alabama, USA ' Department of Finance, Raymond J. Harbert College of Business, Auburn University, Auburn, Alabama, USA ' School of Creative Enterprise and Market Systems, Sorrell College of Business, Troy University, Troy, Alabama, USA

Abstract: We investigate variance risk premiums in the Heston stochastic volatility model with Merton jumps. Risk neutral variance estimates are derived from out-of-the-money option-based integrands. In a controlled simulation setting with model-generated option prices and evenly spaced strikes, our results suggest that 12 or fewer option strikes are sufficient to obtain accurate model-free variance estimates - a finding with practical relevance for researchers working with illiquid underlyings where the available strike grid may be sparse. We find that sample variance is a better estimate of integrated variance than finite quadratic variation under a coarse grid. Model free methods give better estimates than averaged Black-Scholes implied volatilities.

Keywords: variance risk premium; Heston model; Merton jumps; robustness.

DOI: 10.1504/IJFMD.2026.156202

International Journal of Financial Markets and Derivatives, 2026 Vol.10 No.5, pp.1 - 17

Received: 26 May 2026
Accepted: 13 Jul 2026
Published online: 07 Sep 2026 *

Title: The sensitivity of variance risk premium estimates to grid and strike fineness: simulating the Heston model with jumps

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