Erratum for ‘Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility’

ABSTRACT

The purpose of this Erratum is to remedy a minor mistake in Theorems 5.4 and Corollary 5.3 in the article ‘Closed-form approximations for option pricing under stochastic volatility’ [K. Das and N. Langrené, Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility, Stochastics 94(5) (2022), pp. 745–788]. The mistake arose due to neglecting the stochastic nature of the functions $M_{\alpha }(T,K)$ and $M(T,K)$ in Proposition 5.1 and Corollary 5.2 respectively in Das and Langrené [Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility, Stochastics 94(5) (2022), pp. 745–788]. Therefore, expectation must taken on these terms when bounding the error. We state the corrected versions of these results here with proofs.

KEYWORDS:

• Closed-form expansion
• closed-form approximation
• stochastic volatility
• Heston
• GARCH

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by UIC Start-up Research Fund [UICR0700041-22] and Guangdong Provincial Key Laboratory IRADS [2022B1212010006, R0400001-22].