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>

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...

We compute a closed-form expression for the moment generating function fˆ(x;λ,α)=1λEx(eαLτ), where Lt is the local time at zero for standard Brownian motion with reflecting barriers at 0 and b, and τ∼Exp(λ) is independent of W. By analyzing how and where fˆ(x;⋅,α) blows up in λ, a...

We construct a weak solution to the stochastic functional differential equation Xt=x0+∫0tσ(Xs,Ms)dWs, where Mt=sup0≤s≤tXs. Using the excursion theory, we then solve explicitly the following problem: for a natural class of joint density functions μ(y,b), we specify σ(.,.), so that X is a...

For a one-dimensional Itô process Xt=∫0tσsdWs and a general FtX-adapted non-decreasing path-dependent functional Yt, we derive a number of forward equations for the characteristic function of (Xt,Yt) for absolutely and non absolutely continuous functionals Yt. The functional Yt can be the...

We compute the large-maturity smile for the correlated Stein–Stein stochastic volatility model dSt=StYtdWt1,dYt=κ(θ−Yt)dt+σdWt2, dWt1dWt2=ρdt, using the known closed-form solution for the characteristic function of the log stock price given in Schöbel and Zhu (1999). The Stein–Stein...