A comparison principle between rough and non-rough Heston models—with applications to the volatility surface. Issue 6 (2nd June 2020)

• Record Type: Journal Article
• Authors: Keller-Ressel, M.; Majid, A.
• Is Part Of: Quantitative finance. Volume 20:Issue 6(2020)
• Page Start: 919
• Page End: 933
• Publication Date: 2020-06-02
• Subjects: Stochastic volatility -- Heston model -- Rough volatility -- Volatility surface -- Comparison principle -- Moment explosion -- Volterra integral equation; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2020.1714702
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : We present a number of related comparison results, which allow one to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on a comparison principle for certain non-linear Volterra integral equations. Our upper bound for the moment explosion time is different from the bound introduced by Gerhold, Gerstenecker and Pinter [Moment explosions in the rough Heston model. Decisions in Economics and Finance, 2019, 42, 575–608] and tighter for typical parameter values. The results can be directly transferred to a comparison principle for the asymptotic slope of implied variance between rough and non-rough Heston models. This principle shows that the ratio of implied variance slopes in the rough versus non-rough Heston model increases at least with power-law behavior for small maturities.