Introduces a new Heston model with multiple factors.
problem Reconciling classical Heston model with rough Heston model.
method Develops a lifted Heston model with n multi-factors.
result The lifted model provides better fits and faster calibration.
Developed unbiased estimators for Heston model with stochastic interest rates.
problem Estimating the Heston model with stochastic interest rates.
method Combined unbiased estimators with the Heston model and developed a semi-exact log-Euler scheme.
result Convergence rate of O(h) in the L2 norm for a wide range of models. Extends moderate deviations for a randomised Heston model.
problem Analyzing deviations in the Heston model with randomisation.
method Used Gärtner-Ellis theorem and sharp large deviations tools.
result Extended moderate deviations results for the randomised Heston model.
Study shows moment explosion time is finite for rough Heston model under certain conditions.
problem Understanding moment explosion times in the rough Heston model.
method Established upper and lower bounds, computed explosion time algorithm, analyzed critical moments.
result Finite critical moments for all maturities and negative correlation cases.
Improved Heston model produces steeper smile for short maturities.
problem Implied volatility surface does not produce a steep enough smile for short maturities.
method Introduced Stationary Heston model with invariant measure and used Product Recursive Quantization for numerical solution.
result Stationary Heston model produces a steeper smile for short maturities.
We develop high-order approximations for the Heston model.
problem Modeling the Heston model with high accuracy and efficiency.
method Combining approximation schemes on different random grids to achieve any order of convergence.
result Achieve any order of convergence for the Heston model.
Establish C^{1,2} regularity of American value functions in Heston model
problem Regularity of American put options in Heston model
method PDE techniques
result C^{1,2} regularity in exercise domain and smooth-fit principle
Construct geometric interpretation of Heston model using group quantization.
problem Geometric interpretation of Heston model
method Lifted local Lie groupoid formulation
result Geometric interpretation of Heston pricing operator and Riccati equations
Efficiently calibrates Heston model with time-varying parameters for financial derivatives.
problem Calibrating Heston model with time-dependent parameters.
method Simple and numerically efficient approach using semi-analytical formulas and Gauss-Kronrod quadrature.
result Improves Heston model's performance in selected cases.
This paper extends Heston's SV model to include stochastic interest rates.
problem Modeling options with stochastic interest rates.
method Developed a new SV model with stochastic interest rates and derived a semi-explicit formula.
result Derived a semi-explicit formula for option pricing with stochastic interest rates.
Deep neural network improves Heston model calibration accuracy and speed.
problem Calibrating the Heston model with numerical stability issues.
method Gradient-based deep learning framework (DDN) to learn Heston model and its derivatives.
result DDN significantly outperforms non-differential neural networks in calibration accuracy and speed.
AES scheme improves Bermudan and American option pricing for Heston models.
problem Pricing Bermudan and American options under Heston models efficiently.
method AES scheme using non-central chi-square distribution for variance process.
result AES achieves higher accuracy and computational efficiency for Bermudan options.
The Zumbach effect is significant under rough Heston but negligible in classical Heston.
problem Identifying the Zumbach effect in stochastic volatility models.
method Explicit computations of the Zumbach effect under rough Heston model.
result The Zumbach effect is negligible in the classical Heston model but significant under rough Heston.
The Heston model is validated for option pricing using theoretical derivations and empirical market data.
problem Validating the Heston model for accurate option pricing.
method Theoretical derivations and empirical validations using Monte Carlo simulations and machine learning.
result The Heston model is robust and relevant for current financial markets.
Note on instabilities in super-time-stepping methods for Heston model.
problem Instabilities in super-time-stepping methods applied to Heston model.
method Exploration of explicit super-time-stepping schemes (RK-Chebyshev, RK-Legendre) for Heston model.
result Relevance of stability remarks beyond super-time-stepping schemes.
The study finds that specific distributions can be used for risk-neutral valuation in Heston's SV model.
problem Valuation of European options under Heston's stochastic volatility model.
method Analyzing scale-parameter distributions and proving their equivalence to Heston's solution.
result Any RND with mean as the forward spot price that satisfies Heston's option valuation solution must be a member of a scale-family of distributions.
A new model reconciles rough volatility and jumps.
problem Combining rough volatility and jump processes.
method Developed a reversionary Heston model with fast mean reversions and large vol-of-vols.
result The reversionary Heston model converges to Lévy jump processes for certain values of the parameter.
Paper addresses Heston model under violated Feller condition, deriving new change of measure conditions.
problem Investigates Heston model under Feller condition violation.
method Derives sufficient conditions for equivalent martingale measure and true martingale stock price process.
result New conditions for change of measure and martingale properties in Heston model are established.
In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method due to Imai and Tan, a p…
This paper explores the vol-of-vol parameter in the Heston model and its relation to VVIX.
problem Calibrating the Heston model to market data for stable exotic option pricing.
method Four approaches to estimate VVIX in the Heston model: transition density, analytical approximation, and PDE-based.
result Improved calibration stability of the Heston model using the estimated VVIX.
The Heston model is a popular stock price model with stochastic volatility that has found numerous applications in practice. In the present paper, we study the Riemannian distance function associated with the Heston model and obtain explicit formulas for this function using geometrical and analytical methods. Geometric…
The paper solves European option pricing under Heston model using artificial boundary method.
problem Valuation of European call options under Heston stochastic volatility model.
method Asymptotic solution in powers of volatility, artificial boundary method for truncated domain, artificial boundary conditions.
result Artificial boundary conditions improve accuracy and outperform Heston's original boundary conditions.
Comparison results for rough and non-rough Heston models, tighter bounds on moment explosion times.
problem Comparing Heston models with and without roughness.
method Comparison principle for non-linear Volterra integral equations.
result Tighter bounds on moment explosion times for rough Heston models.
Extends Heston model with local volatility for better fit to market volatilities.
problem Fitting stochastic volatility models to market volatilities.
method Adds local volatility term to rough-Heston model, preserving stylized results.
result Provides a proper extrapolation scheme for calibration.
The Volterra Heston model is used to price American options.
problem Pricing American options in the Volterra Heston model.
method Kernel-based approximations and simulation techniques.
result Convergence of American option prices in approximating models to the Volterra Heston model.
Extends rough Heston model solution to general λ.
problem Improving the rough Heston model for various λ values.
method Generalized rational approximation for Mittag-Leffler kernel.
result Convergence of the solution for general λ.
Space mapping calibrates financial models, shown feasible for Heston model.
problem Calibrating financial models with few observable parameters and non-linear constraints.
method Space mapping approach using a coarse surrogate model and fine model calibration.
result Space mapping approach feasible for Heston model calibration.
We extend Heston model with jumps to analyze volatility and implied volatility.
problem Analyzing implied volatility and volatility clustering in financial markets.
method Introducing an affine extension of the Heston model with α-stable jumps. result Examined jump clustering phenomenon and provided a jump cluster decomposition.
This paper extends Heston model to fractional Brownian motion for option pricing.
problem Developing a new financial model for option pricing with fractional Brownian motion.
method Extending Malliavin differentiability to fractional Heston-type model.
result Proves fractional Heston-type model is Malliavin differentiable and derives option pricing expressions.
A new model adds stochastic spot/volatility correlation to Heston model for better exotic pricing.
problem Improving exotic option pricing in foreign exchange markets.
method Developed a Double Heston model with stochastic spot/volatility correlation, an affine model.
result The new model increases prices of out-of-the-money knockout options and one touch options.
Efficient simulation scheme for rough Heston model reduces computational cost.
problem Accurate and efficient simulation of the rough Heston model for option pricing.
method Weak simulation scheme based on Markovian approximations of the rough Heston process.
result The new scheme exhibits second order weak convergence with linear computational cost.
Proposes a simplified Heston model for VIX and S&P 500 options calibration.
problem Calibrating volatility models for VIX and S&P 500 options.
method Perturbation technique to derive a first-order approximation of option prices.
result Efficient calculation of option prices using Fourier integrals and ODE solutions.
Optimizes variance reduction in Heston model using large and moderate deviations.
problem Improving variance reduction in stochastic volatility models.
method Large and moderate deviations theory applied to Heston model.
result Derives closed-form solutions for optimal change of measure.
This research improves option pricing models using Heston, GARCH, and jump diffusion models.
problem Inaccurate option pricing due to Black-Scholes assumptions.
method Monte Carlo simulation, GARCH model, Heston model, Merton jump-diffusion model.
result Heston model produces estimates closer to market prices, Merton model performs well for volatile assets, GARCH model improves volatility forecasts.
A new FFT method for Heston model option pricing with explicit error bounds.
problem Efficiently pricing European options in the Heston model with high accuracy.
method Convolution-FFT method leveraging a continuously differentiable joint characteristic function.
result Explicit error bounds for FFT-based convolution method in Heston model.
The paper derives formulas for pricing geometric Asian options in the Volterra-Heston model.
problem Pricing geometric Asian options in the Volterra-Heston model.
method Derives semi-closed formulas using Fourier transforms and Riccati-Volterra equations.
result Derives formulas for pricing geometric Asian options with fixed and floating strikes.
Market maker optimizes SPX and VIX spread using quadratic rough Heston model.
problem Maximizing profit from SPX and VIX spread while managing inventory risk.
method Uses quadratic rough Heston model to optimize multi-asset market making problem, approximating high-dimensional optimization.
result Asymptotic closed-form solution for optimization problem.
Non-unique option pricing in Heston model analyzed mathematically.
problem Non-uniqueness of call option prices in the Heston model.
method Analysis of degenerate parabolic equations in the context of option pricing.
result Construction of a new example demonstrating the accuracy of a uniqueness theorem.
Investigates Merton's portfolio problem in a rough stochastic environment with Volterra Heston model.
problem Optimizing investment strategies in a non-Markovian, non-semimartingale stochastic environment.
method Solves the portfolio optimization problem using the martingale optimality principle and auxiliary random process.
result Derives semi-closed form solutions for optimal strategies under power and exponential utilities.
Paper compares stock price prediction models using Heston and Geometric Brownian Motion.
problem Predicting stock prices accurately.
method Developed Heston and Geometric Brownian Motion models using Ito's lemma and Euler-Maruyama methods.
result Models outperform statistical indicators in predicting stock prices.
We propose a hybrid tree-finite difference method in order to approximate the Heston model. We prove the convergence by embedding the procedure in a bivariate Markov chain and we study the convergence of European and American option prices. We finally provide numerical experiments that give accurate option prices in th…
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…
Model monthly VIX and stock returns using log-Heston model.
problem Modeling monthly VIX and stock index returns accurately.
method Log-Heston model applied to logarithm of VIX as an autoregression, normalizing stock returns by VIX.
result Model captures independent, identically distributed Gaussian stock returns after normalization.
Deep learning calibrates a rough Heston model to match implied volatilities.
problem Calibrating the quadratic rough Heston model to match market implied volatilities.
method Multi-factor approximation and deep learning for efficient calibration.
result The model accurately reproduces SPX and VIX implied volatilities.
We study a hybrid tree-finite difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the rel…
The Heston model optimizes portfolio management based on real market data.
problem Choosing between active and passive investment strategies.
method Calibrated Heston model to real stock market data.
result Passive strategy can outperform active strategy depending on market parameters.
Expanding the rough Heston model in H
problem Analyzing the dependence of the fractional Riccati equation on the Hurst parameter H method Deriving a Taylor expansion of the Riccati solution in H result Local uniform convergence and analyticity of the fractional Riccati solution
This work presents an exact solution to the generalized Heston model, where the model parameters are assumed to have linear time dependence The solution for the model in expressed in terms of confluent hypergeometric functions.