We consider the fractional Heston model originally proposed by Comte, Coutin, and Renault
[Ann. Finance, 8 (2012), pp. 337--378]. Inspired by recent groundbreaking work on rough …

We characterize the asymptotic smile and term structure of implied volatility in the Heston
model at small maturities. Using saddlepoint methods we derive a small-maturity expansion …

Asymptotic analysis of stochastic stock price models is the central topic of the present
volume. Special examples of such models are stochastic volatility models, that have been …

The implied volatility surface (IVS) is a fundamental building block in computational finance.
We provide a survey of methodologies for constructing such surfaces. We also discuss …

This paper proposes “implied stochastic volatility models” designed to fit option-implied
volatility data and implements a new estimation method for such models. The method is …

We characterize the behavior of the Rough Heston model introduced by Jaisson and
Rosenbaum (2016, Ann. Appl. Probab., 26, 2860–2882) in the small‐time, large‐time, and …

We calibrate Heston stochastic volatility model to real market data using several optimization
techniques. We compare both global and local optimizers for different weights showing …

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 …

This note explores the behaviour of the implied volatility of a European call option far from
maturity. Asymptotic formulae are derived with precise control over the error terms. The …

We reconcile rough volatility models and jump models using a class of reversionary Heston
models with fast mean reversions and large vol-of-vols. Starting from hyper-rough Heston …