We build on of the work of Henry-Labordµere and Lewis on the small-time behaviour of the return distribution under a general local-stochastic volatility model with zero correlation. We do this using the Freidlin-Wentzell theory of large deviations for stochastic differential equations, and then...

Using the Gartner-Ellis theorem from large deviation theory, we characterize the leading-order behaviour of call option prices under the Heston model, in a new regime where the maturity is large and the log-moneyness is also proportional to the maturity. Using this result, we then derive the...

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...

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the implied volatility function. The proof is based on...

This note identifies a gap in the proof of Corollary 2.4 in [2], which arises because the essential smoothness of the family (Xt/t) can fail for the log-spot process X in the Heston model, and describes how to circumvent the issue by applying a standard argument from large deviation theory

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>