arXiv research

No-arbitrage constraints on implied variance slope are weak, leading to almost guaranteed arbitrage in many cases.

This paper examines Bachelier implied volatility at extreme strikes.

Symbolic regression finds simple formulas for implied volatility.

We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter $H < 1/2$. This regime recently attracted a lot of attention both from the statistical and option pricing point of view. With focus on the latter, we sharpen the large de…

Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and Sølna (2011, CUP) analyzes models in which the volatility of the underlying i…

We derive a small-time expansion for out-of-the-money call options under an exponential Levy model, using the small-time expansion for the distribution function given in Figueroa-Lopez & Houdre (2009), combined with a change of numéraire via the Esscher transform. In particular, we quantify find that the effect of a no…

Study short-maturity Asian option pricing in LSV models using large deviations theory.

Derives short-term option pricing asymptotics in local-stochastic volatility models.

This paper optimizes importance sampling for rare-event options pricing under the Heston model.

Using the large deviation principle (LDP) for a re-scaled fractional Brownian motion $B^H_t$ where the rate function is defined via the reproducing kernel Hilbert space, we compute small-time asymptotics for a correlated fractional stochastic volatility model of the form $dS_t=S_tσ(Y_t) (\barρ dW_t +ρdB_t), \,dY_t=dB^H…

We compute a sharp small-time estimate for implied volatility under a general uncorrelated local-stochastic volatility model. For this we use the Bellaiche \cite{Bel81} heat kernel expansion combined with Laplace's method to integrate over the volatility variable on a compact set, and (after a gauge transformation) we …

The method constructs arbitrage-free option surfaces from noisy quotes using Chebyshev bases and a fog post-fit layer.

We characterize the behaviour of the Rough Heston model introduced by Jaisson\&Rosenbaum \cite{JR16} in the small-time, large-time and $α\to 1/2$ (i.e. $H\to 0$) limits. We show that the short-maturity smile scales in qualitatively the same way as a general rough stochastic volatility model (cf.\ \cite{FZ17}, \cite{FGP…