We add some rigour to the work of Henry-Labordère (2009; Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing (London and New York: Chapman & Hall)), Lewis (2007; Geometries and Smile Asymptotics for a Class of Stochastic Volatility Models. Available at <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink"...</ext-link>

The papers (Forde and Jacquier in Finance Stoch. 15:755–780, <CitationRef CitationID="CR1">2011</CitationRef>; Forde et al. in Finance Stoch. 15:781–784, <CitationRef CitationID="CR2">2011</CitationRef>) study large-time behaviour of the price process in the Heston model. This note corrects typos in Forde and Jacquier (Finance Stoch. 15:755–780, <CitationRef CitationID="CR1">2011</CitationRef>), Forde et al. (Finance...</citationref></citationref></citationref>

This note studies an issue relating to essential smoothness that can arise when the theory of large deviations is applied to a certain option pricing formula in the Heston model. The note identifies a gap, based on this issue, in the proof of Corollary 2.4 in \cite{FordeJacquier10} and describes...

We show that if the discounted Stock price process is a continuous martingale, then there is a simple relationship linking the variance of the terminal Stock price and the variance of its arithmetic average. We use this to establish a model-independent upper bound for the price of a continuously...

We rigorize the work of Lewis (2007) and Durrleman (2005) on the small-time asymptotic behavior of the implied volatility under the Heston stochastic volatility model (Theorem 2.1). We apply the Gärtner-Ellis theorem from large deviations theory to the exponential affine closed-form expression...