Large-Maturity Regimes of the Heston Forward Smile
We provide a full characterisation of the large-maturity forward implied volatility smile in the Heston model. Although the leading decay is provided by a fairly classical large deviations behaviour, the algebraic expansion providing the higher-order terms highly depends on the parameters, and different powers of the maturity come into play. As a by-product of the analysis we provide new implied volatility asymptotics, both in the forward case and in the spot case, as well as extended SVI-type formulae. The proofs are based on extensions and refinements of sharp large deviations theory, in particular in cases where standard convexity arguments fail.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Small-time, large-time and $H\to 0$ asymptotics for the Rough Heston model
We characterize the behaviour of the Rough Heston model introduced by Jaisson\&Rosenbaum \cite{JR16} in the small-time, large-time and $\alpha \to 1/2$ (i.e. $H\to 0$) limits. We show that the short-maturity smile scales…
Asymptotic Smiles for an Affine Jump-Diffusion Model
In this paper, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion model. Let log stock price under risk-neutral measure follow an affine jump-diffusion model, we show that an explicit for…
modelSimulation of square-root processes made simple: applications to the Heston model
We introduce a simple, efficient and accurate nonnegative preserving numerical scheme for simulating the square-root process. The novel idea is to simulate the integrated square-root process first instead of the square-r…
Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration
In energy markets, joint historical and implied calibration is of paramount importance for practitioners yet notoriously challenging due to the need to align historical correlations of futures contracts with implied vola…
Lifting the Heston model
How to reconcile the classical Heston model with its rough counterpart? We introduce a lifted version of the Heston model with n multi-factors, sharing the same Brownian motion but mean reverting at different speeds. Our…
model