Related papers: A note on essential smoothness in the Heston model
We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…
Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive modified Bessel function evaluations. We propose a new exact simulation scheme without the…
We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on…
This work examines a stochastic volatility model with double-exponential jumps in the context of option pricing. The model has been considered in previous research articles, but no thorough analysis has been conducted to study its quality…
Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under…
The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state…
The Heston stochastic volatility model is a standard model for valuing financial derivatives, since it can be calibrated using semi-analytical formulas and captures the most basic structure of the market for financial derivatives with…
This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least squares problem. We exploit a suitable representation of the Heston…
Robust, or model-independent properties of the variance swap are well-known, and date back to Dupire and Neuberger, who showed that, given the price of co-terminal call options, the price of a variance swap was exactly specified under the…
We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the…
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…
We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and…
We study Euler-type discrete-time schemes for the rough Heston model, which can be described by a stochastic Volterra equation (with non-Lipschtiz coefficient functions), or by an equivalent integrated variance formulation. Using weak…
We extend upon the saddle-point equation presented in [1] to derive large-time model-implied volatility smiles, providing its theoretical foundation and studying its applications in classical models. As long as characteristic function…
We consider a class of asset pricing models, where the risk-neutral joint process of log-price and its stochastic variance is an affine process in the sense of Duffie, Filipovic and Schachermayer [2003]. First we obtain conditions for the…
We extend previous large deviations results for the randomised Heston model to the case of moderate deviations. The proofs involve the G\"artner-Ellis theorem and sharp large deviations tools.
We perform a classification of the Lie point symmetries for the Black--Scholes--Merton Model for European options with stochastic volatility, $\sigma$, in which the last is defined by a stochastic differential equation with an…
We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options.…
We consider a large market model of defaultable assets in which the asset price processes are modelled as Heston-type stochastic volatility models with default upon hitting a lower boundary. We assume that both the asset prices and their…
In the present work, the European option pricing SWIFT method is extended for Heston model calibration. The computation of the option price gradient is simplified thanks to the knowledge of the characteristic function in closed form. The…