The article reviews how to set stochastic volatility model parameters.
problem Choosing parameters for stochastic volatility models.
method Examines existing literature on various methods.
result Different approaches to setting stochastic volatility parameters.
The paper provides a formula for pricing volatility swaps with stochastic volatility, jumps, and stochastic intensity.
problem Valuation of volatility swaps in markets with stochastic volatility, jumps, and stochastic intensity.
method The paper uses the stochastic volatility model with jumps and stochastic intensity, and the Feynman-Kac theorem to derive a partial integral differential equation. Discrete and continuous sampled volatility swap pricing formulas are obtained using transform techniques.
result The paper delivers a pricing formula for volatility swaps under stochastic volatility with jumps and stochastic intensity.
We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do…
This paper compares two extensions of the Heston model for option pricing.
problem Improving the accuracy of option pricing models.
method Empirical analysis and non-linear least square optimization of parameters.
result The multiscale stochastic volatility model outperforms the Heston model.
Paper quantifies how past stock returns inform about volatility and future returns.
problem Inferring volatility and future returns from past returns in stochastic volatility models.
method Quantifies mutual information between past and future stock returns and volatility.
result Past stock returns provide significant information about future volatility and returns.
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
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…
Entropy-minimal measure calculated for a stochastic volatility model.
problem Calculating the entropy-minimal equivalent martingale measure in a stochastic volatility model.
method Revised related theory, calculated entropy-minimal measure.
result Entropy-minimal measure for the exponential Ornstein-Uhlenbeck model.
Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.
problem Calibrating local volatility models with stochastic drift and diffusion.
method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.
result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.
Study on Kyle's model with stochastic liquidity impacts asset volatility.
problem Impact of stochastic volatility of noise trading on asset volatility.
method Construct equilibrium for continuous-time Kyle's model with stochastic liquidity.
result In equilibrium, Kyle's Lambda and its inverse are submartingales.
The paper shows robustness of Hilbert space-valued stochastic volatility models to perturbations.
problem Robustness of Hilbert space-valued stochastic volatility models to measurement or approximation errors.
method Quantifying the error induced by volatility perturbations and studying robustness of volatility process with finite dimensional approximations.
result Explicit bounds for the induced error in terms of approximation of the underlying parameter.
Proposes uncertain volatility models with fluctuating stochastic bounds for improved accuracy.
problem Improving accuracy in modeling volatility with fluctuating bounds.
method Introduces stochastic bounds that fluctuate according to a stochastic volatility process, applying perturbation analysis to reduce complexity.
result The method provides a significant computational advantage and performs well even with moderately slow varying bounds.
The study models geophysical and financial volatility using GARCH and stochastic volatility models.
problem Forecasting volatility in geophysical and financial time series.
method Presented a class of volatility models with time-varying parameters, using GARCH and stochastic volatility models.
result Stochastic volatility model outperforms GARCH (1, 1) in forecasting one-step-ahead volatility.
The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the exist…
Study on asset price density and option pricing under stochastic volatility models.
problem Understanding asset price density and option pricing in stochastic volatility models.
method Small-time Edgeworth expansion and limit theorems for implied volatility.
result Asymptotic expansions of put option prices and at-the-money implied volatilities.
We expand volatility models for rough stochastic volatility.
problem Modeling rough stochastic volatility.
method Vol-of-vol expansion for potentially infinite dimensional models.
result Explicit representations of push-down Malliavin weights.
A new volatility model blends large and small volatility features.
problem Modeling stock returns and realized volatility.
method Combines multiplicative and Heston models for volatility.
result Steady-state distribution is power-law at both large and small volatilities.
The chapter evaluates volatility and variance swap pricing under stochastic volatility models.
problem Pricing of volatility derivatives under stochastic volatility models.
method Uses convexity correction approximation, Laplace transform, and Markov chain Monte Carlo algorithm.
result Shows the impact of jumps on volatility derivatives pricing and compares different pricing approaches.
Derives short-term option pricing asymptotics in local-stochastic volatility models.
problem Short-term option pricing in local-stochastic volatility models.
method Large deviations theory and variational methods.
result Explicit series expansions for implied volatility and asymptotic results for European and VIX options.
Approximates derivative pricing under fractional stochastic volatility.
problem Derivative pricing under fractional stochastic volatility model.
method Approximate expression derived from deterministic functions and fractional Ornstein-Uhlenbeck process.
result Numerical simulations show the feasibility and effect of long-range dependencies on derivative prices.
Study large deviations in fractional volatility models with non-Gaussian volatility.
problem Large deviations in fractional volatility models with non-Gaussian volatility.
method Established a small-noise large deviation principle for log-price.
result Logarithmic call price asymptotics for large strikes in a special case.
Paper improves stochastic collocation for local volatility models.
problem Improving local volatility models for assets with boundaries.
method Applied stochastic collocation to lognormal distributions, derived analytical local volatility.
result Simple analytical Dupire local volatility derived from option prices.
The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.
problem Large deviation principles for stochastic volatility models with reflection.
method Sample path and small-noise large deviation principles for the log-price process.
result Asymptotic behavior of binary barrier options and call prices in the small-noise regime.
Paper generalizes pricing and hedging of volatility swaps in stochastic models.
problem Pricing and hedging of volatility swaps in stochastic volatility models.
method Generalizes zero vanna approximation to seasoned swaps, derives hedges using vanilla options and variance swaps.
result Pricing and hedging of volatility swaps are made practical and robust.
Paper approximates rough stochastic local volatility models for efficient computation.
problem No unified method for rough stochastic local volatility models.
method Semimartingale and continuous-time Markov chain approximation.
result Fast CTMC algorithm with weak convergence proved.
A new fast method simulates stochastic volatility models.
problem Simulating stochastic volatility models efficiently.
method Karhunen-Loève expansions to express stochastic volatility as sine series, followed by analytical derivation of integrals.
result Simulation is several hundred times faster than existing methods.
Study provides LDP for non self-similar stochastic volatility models.
problem Analyzing non self-similar stochastic volatility models.
method Short-time large deviation principle (LDP) for models with Volterra process.
result Derives consequences for option prices, implied volatility surfaces, and skew.
Expands method for pricing foreign exchange options under stochastic volatility and interest rates.
problem Approximating pricing of foreign exchange options with no exact formula.
method Directly expands the expectation value of payoff function with respect to the volatility of volatility, then uses it to price options in the stochastic volatility model.
result Shows numerically comparable results to Grzelak et al. (2012) using characteristic function approximation.
Exact solutions found for a new SV model with stationary volatility.
problem Finding exact solutions for a new SV model.
method Analytical solutions for transition probability density, option values, and martingale defect.
result First example of an SV model with exact solutions, GBM volatility, and stationary volatility.
We present a new simple method of estimating stochastic volatility and its volatility. This method is applicable to both cross-sectional and time-series data. Moreover, this method does not require volatility data series.
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.
Study on implied volatility of Asian options with stochastic volatility.
problem Understanding the implied volatility of Asian options under stochastic volatility models.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for the implied volatility and skew.
result Developed short-maturity asymptotic formulas for the skew of the implied volatility, which depends on the roughness of the volatility model.
Enhanced volatility forecasting using options data and rough volatility model.
problem Improving realized volatility forecasting accuracy.
method Infer spot volatility from options data using rough stochastic volatility model, accelerate estimation with deep learning, benchmark against traditional models.
result Augmented HAR-RV-RHeston model outperforms traditional models in daily and long-term forecasting.
New method for precise option pricing in stochastic volatility models.
problem Analyzing large classes of stochastic volatility models for robust option pricing.
method Theory of regularity structures and Laplace method on the space of models.
result Precise asymptotics for European options in rough volatility models.
Research forecasts electricity spot prices using stochastic volatility models.
problem Forecasting day-ahead electricity prices in a spot market.
method Exploring and enriching a baseline stochastic volatility model with exogenous regressors.
result A better fitting model confirmed by out-of-sample forecasts.
Neural model improves volatility estimation and prediction in finance.
problem Improving volatility estimation and prediction in finance.
method Integrates deep neural networks with stochastic volatility models.
result Proposed model outperforms existing methods on average negative log-likelihood.
We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential Lévy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time through common driving factors -- one fast-varying and one slow-varying. Using Four…
Diamonds help compute volatility models efficiently.
problem Computing volatility models in forward variance form.
method Application of diamond trees and forests.
result Efficient computation of volatility models.
Existence of calibrated local stochastic volatility models proven for non-regular coefficients.
problem Existence of calibrated local stochastic volatility models in finance.
method Investigation of McKean--Vlasov equations with minimal continuity assumptions on coefficients, providing existence and propagation of chaos results.
result Existence of calibrated local stochastic volatility models for appropriate stochastic volatility parameters.
The paper analyzes implied volatility for European and Asian options under stochastic volatility Bachelier model.
problem Analyzing implied volatility for European and Asian options under stochastic volatility.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for implied volatility and skew.
result The paper provides a short maturity asymptotic formula for the skew of implied volatility that depends on the roughness of the volatility model.
Pricing barrier options with a new stochastic volatility model.
problem Financial option pricing under volatility effects.
method 2-hypergeometric stochastic volatility model, regular perturbation method.
result Explicit and easily computable formula for barrier options.
New model captures time-varying volatility with stochastic exponential tails.
problem Capturing time-varying volatility and stochastic skewness in financial markets.
method Normal Tempered Stable distribution with time-varying parameter.
result Model better explains market option prices with stochastic exponential tails.
Efficiently prices options in stochastic volatility models using sparse grids.
problem Option pricing in stochastic volatility models.
method Sparse grid high-order ADI scheme for second-order in time and fourth-order in space.
result Computational efficiency gains confirmed by numerical experiments.
Corrects a mistake in a proof about large portfolios of stochastic volatility models.
problem Problems with a proof in a paper about large portfolios of stochastic volatility models.
method Reestablishes a weaker version of Theorem 3.1 and redevelops regularity theory.
result Most regularity results are replaced by slightly weaker ones.
Study on stochastic volatility models with external shocks triggering jump cascades.
problem Analyzing the impact of external shocks on jump dynamics in stochastic volatility models.
method Establishing scaling limits for a class of stochastic volatility models with self-exciting jump dynamics.
result External shocks can trigger endogenous jump cascades in asset returns and volatility.
Introduces σ-Cell for improved financial volatility forecasting.
problem Improving volatility forecasting in financial markets.
method Combines GARCH and deep learning, incorporating stochastic layers and time-varying parameters.
result Demonstrates superior forecasting accuracy compared to traditional models.
Study exchange option pricing with stochastic volatility and correlation.
problem Pricing exchange options under stochastic volatility and correlation.
method Approximation using a closed-form solution with Taylor expansion.
result Numerical results show the effectiveness of the proposed method.
The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. …