A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Extends Heston model with local volatility for better fit to market volatilities.
This paper explores the vol-of-vol parameter in the Heston model and its relation to VVIX.
A new model adds stochastic spot/volatility correlation to Heston model for better exotic pricing.
Note on instabilities in super-time-stepping methods for Heston model.
This research improves option pricing models using Heston, GARCH, and jump diffusion models.
We present a detailed analysis of \emph{observable} moments based parameter estimators for the Heston SDEs jointly driving the rate of returns and the squared volatilities . Since volatilities are not directly observable, our parameter estimators are constructed from empirical moments of realized volatilitie…
Deep learning calibrates a rough Heston model to match implied volatilities.
In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a simpler expression for th…
Derives a pricing formula for VIX options using a new stochastic volatility model.
Adaptive Heston model calibration using PCRLB and switching filters.
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…
A new model reconciles rough volatility and jumps.
Researchers prove a new measure for a financial volatility model.
It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Br…
We consider a model of stochastic volatility which combines features of the multiplicative model for large volatilities and of the Heston model for small volatilities. The steady-state distribution in this model is a Beta Prime and is characterized by the power-law behavior at both large and small volatilities. We disc…
Paper derives Thiele's equation for unit-linked policies in a stochastic volatility model.
This paper extends Heston model to fractional Brownian motion for option pricing.
Using microscopic price models based on Hawkes processes, it has been shown that under some no-arbitrage condition, the high degree of endogeneity of markets together with the phenomenon of metaorders splitting generate rough Heston-type volatility at the macroscopic scale. One additional important feature of financial…
Previous literature has identified an effect, dubbed the Zumbach effect, that is nonzero empirically but conjectured to be zero in any conventional stochastic volatility model. Essentially this effect corresponds to the property that past squared returns forecast future volatilities better than past volatilities foreca…
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 a comparison principle for certain non-linear Volterra integral equations. Our u…
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 order terms in the large maturity expansion of the implied volatility function. The proof is based on saddlepoint methods and classical …
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for European option prices. The resulting pricing formulas are semi-analytic, in th…
New model captures asymmetric rough volatility with Zumbach effect.
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 simple structure in time-direction. However, extending the model to the case of time-…
A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking at short maturities. For that reason, we introduce the Stationary Heston model where we replace the deterministic initial condition of the volatility by its invariant measure and show,…
Develops a novel framework for pricing variance swaps in multi-asset stochastic volatility models.
Optimizes variance reduction in Heston model using large and moderate deviations.
Investors face constraints in Heston's model; optimal allocation differs from naive capped strategy.
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and calibration of implied volatility is the addition of a few other factors to the volatil…
In 'A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options', Heston proposes a Stochastic Volatility (SV) model with constant interest rate and derives a semi-explicit valuation formula. Heston also describes, in general terms, how the model could be extended to inc…
The study finds that specific distributions can be used for risk-neutral valuation in Heston's SV model.
Estimates Heston model with jumps in asset prices using Bayesian regression and particle filtering.
Proposes a new agent-based model for deep hedging that outperforms existing models.
A new method speeds up option pricing under Heston's stochastic volatility model.
Efficiently simulates the Heston model with large time steps using a novel method.
The Heston model is validated for option pricing using theoretical derivations and empirical market data.
A parsimonious generalization of the Heston model is proposed where the volatility-of-volatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al (2011, CUP) to derive a first order approximation of the price of options on a stock and its volatility index. This approximation is given by…
We address the information content of European option prices about volatility in terms of the Fisher information matrix. We assume that observed option prices are centred on the theoretical price provided by Heston's model disturbed by additive Gaussian noise. We fit the likelihood function on the components of the VIX…
We consider the fractional Heston model originally proposed by Comte, Coutin and Renault. Inspired by recent ground-breaking work on rough volatility, which showed that models with volatility driven by fractional Brownian motion with short memory allows for better calibration of the volatility surface and more robust e…
We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian São Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the ana…
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 volatility in order to work out the problem for the return alone regardless volatilit…
Deep learning accelerates Heston model calibration.
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model…
Model monthly VIX and stock returns using log-Heston model.
Quantum algorithm for multi-asset option pricing under different volatility models.
When dealing with Heston's stochastic volatility model, the change of measure from the subjective measure P to the objective measure Q is usually investigated under the assumption that the Feller condition is satisfied. This paper closes this gap in the literature by deriving sufficient conditions for the existence of …
This paper analyzes model risk in American put options using Heston volatility model.
This paper uses deep learning to price American options under stochastic volatility.