New formulas derived for variance gamma model option pricing.
problem Option pricing for the variance gamma model.
method Combining randomization method and fractional derivatives.
result Closed-form formulas for European options.
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48 results for “fractional Variance Gamma model”
Option Pricing with Time-Changed Fractional Brownian Motion: A Fractional Variance Gamma Modelq-fin.MF
A new model uses time-changed fractional Brownian motion to price financial options.
problem Non-semimartingale nature of fractional Brownian motion limits option pricing.
method Develops a time-changed fractional Brownian motion and a fractional Variance Gamma model.
result Empirical analysis shows consistent Hurst exponent of approximately 0.45.
The paper analyzes a five-parameter Variance-Gamma model for European option pricing.
problem Developing a stochastic volatility model for accurate European option pricing.
method Introduced a five-parameter Variance-Gamma model and applied it to empirical data.
result The five-parameter VG model produces underpriced OTM and overpriced ITM options compared to the Black-Scholes model.
The article prices exchange options using variance gamma-like models.
problem Pricing exchange options under specific stochastic processes.
method Derives formulas for variance gamma and variance gamma++ processes, constructs multidimensional versions, calibrates parameters with real data.
result Closed formulas and numerical methods for evaluating exchange options.
The paper uses the variance-gamma model to price options and explain excess kurtosis.
problem Explaining excess kurtosis in stock price data.
method Random-time subordination, Laplace distribution, Esscher transform.
result The variance-gamma model explains excess kurtosis in log-returns data.
Study shows variance gamma model outperforms Black-Scholes for USD-INR currency options.
problem Complex pricing of currency options with multi-assets.
method Examined USD-INR currency options, tested several models, compared performance.
result Variance gamma model outperforms Black-Scholes model in various volatility regimes.
The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.
problem Creating an arbitrage-free interpolation for option pricing models.
method Generalizing the local variance gamma model to a piecewise quadratic local variance function.
result The quadratic model results in an arbitrage-free interpolation of class C3, reducing knots and computational cost.
W-shaped vol curves in liquid options can be modeled with two variance-gamma models.
problem Reproducing W-shaped implied volatility curves in liquid option markets.
method Using a mixture of two variance-gamma models.
result W-shaped vol curves can be generated with fewer distributions (two) compared to lognormal models (at least three).
Develops a fast method for pricing American options under variance gamma model.
problem Inefficient methods for pricing American options under variance gamma model.
method Inspired by quadratic approximation method, uses machine learning on pre-calculated quantities to reduce error.
result Proposed method is efficient and accurate for practical use.
Introduces a new Lévy process for modeling illiquid markets.
problem Modeling dynamic of assets in illiquid markets.
method Introduces Variance Gamma++ process, a new Lévy process, and provides efficient path simulation algorithms.
result Efficient pricing formula and parameter estimation for European options.
Paper presents a multinomial method for option pricing under Variance Gamma.
problem Option pricing under non-standard stochastic processes.
method Discrete time Markov chain approximation of continuous time Variance Gamma process.
result Pricing American and Bermudan options is feasible with this method.
New calibration methods improve fitting of weak variance-alpha-gamma process.
problem Improving fitting of a multivariate Lévy process.
method Comparison of three calibration methods: method of moments, maximum likelihood estimation, and digital moment estimation.
result Maximum likelihood estimation produces a better fit when a specific condition holds, while digital moment estimation produces a better fit when the condition is violated.
Unified framework SVAM learns GLMs robustly to adversarial label corruption.
problem Learning GLMs under adversarial label corruption.
method SVAM framework based on variance reduction technique.
result Provable model recovery guarantees superior to state-of-the-art.
Closed pricing formulas for Variance Gamma model payoffs.
problem Pricing path-independent payoffs in the Variance Gamma model.
method Mellin transform theory and multidimensional complex analysis.
result Closed-form pricing formulas with accelerated convergence for short-term options.
Extends Local Variance Gamma model with geometric Brownian motion and piecewise linear local variance.
problem Modeling volatility dynamics in financial markets.
method Develops a geometric version of the Local Variance Gamma model with drift and piecewise linear local variance functions.
result Derives an ordinary differential equation for option prices and solves it in closed form.
Expanded Local Variance Gamma model adds drift and simplifies calibration.
problem Calibration of complex local volatility surfaces.
method Adding drift to the underlying process, deriving an ODE, piecewise linear and constant local variance, closed-form solution using hypergeometric functions.
result Calibration to market smiles can be done term-by-term and is fast.
Modeling stock returns and volatility using a bivariate gamma generalized Laplace law.
problem Analyzing stock returns and volatility using a new statistical model.
method Maximum likelihood estimation for a bivariate generalized Laplace distribution, simplifying to linear regression.
result Explicit estimators derived with nonstandard convergence rates for certain parameter configurations.
We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is time varying and follows an affine Garch model, trying to capture persistence o…
Study simulates Variance Gamma processes for energy derivatives pricing.
problem Simulating Variance Gamma processes for accurate energy derivative pricing.
method Three-step procedure to relate self-decomposability to increments, derived from Qu et al. (2019). Exact simulation of skeleton of Variance Gamma and symmetric Variance Gamma driven Ornstein-Uhlenbeck processes.
result Exact simulation of Variance Gamma and related processes without numerical inversion.
The paper prices energy spread options using a complex stochastic model.
problem Pricing energy spread options with specific stochastic dynamics.
method Uses an exponential Ornstein-Uhlenbeck process driven by variance gamma processes, applying the Esscher transform and FFT method.
result Derives an analytical formula for pricing forwards and spread options.
Study proposes a nonlocal approximation of the Willmore functional using fractional Allen-Cahn energies.
problem Approximating the Willmore functional using nonlocal methods.
method Gamma-convergence and fractional Laplacian analysis in Fermi coordinates.
result Proves -limsup estimate for the proposed nonlocal approximation.
Thompson sampling used for linear bandits with normal-gamma priors.
problem Optimizing decisions in uncertain environments with linear dependencies and unknown parameters.
method Bayesian Thompson sampling with multivariate normal-gamma priors.
result Derivation of a Bayesian regret bound for the approach.
Wealth distribution: To be or not to be a Gamma?physics.soc-ph
We review some aspects, especially those we can tackle analytically, of a minimal model of closed economy analogous to the kinetic theory model of ideal gases where the agents exchange wealth amongst themselves such that the total wealth is conserved, and each individual agent saves a fraction (0 < lambda < 1) of wealt…
A Monte Carlo method for pairs trading on mean-reverting spreads with Lévy processes.
problem Trading on mean-reverting spreads with flexible models.
method Monte Carlo simulation with variance gamma and alpha-gamma driving processes.
result Optimal trading strategies are affected by model parameters and correlation.
Develops Bayesian inference methods for gamma models.
problem Challenges in inference for models with gamma functions.
method Data augmentation scheme using Exponential Reciprocal Gamma distributions.
result Scalable EM and MCMC algorithms developed.
New pricing model uses variance-gamma process for financial assets.
problem Traditional pricing models need improvement for complex financial assets.
method Developed a new class of models based on variance-gamma process.
result The new model can price a variety of financial assets effectively.
Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being a special case of limited dependent data, the models also apply to variables tha…
Develops a data augmentation method for models with gamma functions.
problem Models with gamma functions lack natural conjugate priors, complicating inference and prediction.
method Derives Pólya Inverse Gamma distributions and applies them to scalable EM and MCMC algorithms.
result Provides scalable algorithms for inference and prediction in models with gamma functions.
Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance is poor in nonparametric models. We take a small-variance asymptotics (SVA) appr…
The mixed-fractional CEV model improves CDS pricing by accounting for default risk.
problem Improving the pricing of Credit Default Swaps (CDS) by accounting for default risk.
method Using a mixed-fractional Brownian motion to model the Constant Elasticity of Variance (CEV) model.
result The mixed-fractional CEV model yields more realistic CDS spreads and default probabilities.
The paper explores risk-minimization for exponential additive models, providing mathematical expressions and numerical examples.
problem Risk-minimization in incomplete markets for exponential additive models.
method Derive explicit mathematical expressions for local risk-minimization strategies in exponential additive models.
result Provide necessary conditions for deriving expressions and confirm integrability conditions for specific models.
FPG uses fractional calculus for efficient reinforcement learning with long-term memory.
problem High variance and inefficient sampling in standard policy gradient methods for long-term temporal modeling.
method Fractional Policy Gradients (FPG) incorporating Caputo fractional derivatives for power-law temporal correlations.
result Achieves asymptotic variance reduction of order O(t^(-alpha)) and sample efficiency gains.
This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model …
On the relative performance of some parametric and nonparametric estimators of option pricesq-fin.CP
Study compares parametric and Hermite-based models for option pricing.
problem Empirical performance of option price estimators.
method Examines parametric and nonparametric models, focusing on variance-gamma and Heston models.
result Hermite-based models can outperform Heston model in pricing errors.
The paper calibrates a model to market quotes efficiently and arbitrage-free.
problem Calibrating a model to market option quotes efficiently and without arbitrage.
method Piecewise-linear local variance function for efficient calibration.
result Arbitrage-free interpolation of class achieved under one millisecond.
A new distribution family extends the -stable distribution with a degree of freedom parameter.
problem Lack of moments in the -stable distribution.
method Wright function framework to combine and extend distribution families.
result Generalized -stable distribution with valid moments.
New process from fractional BM and OU process yields simpler variance.
problem Simpler model for autocovariance structure.
method Construct new process using fractional BM and OU process, analyze increments.
result Variance of new process easier to compute than FARIMA.
While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key challenge in either setting is controlling the variance of gradient estimates: rec…
New process explains asset volatility patterns.
problem Explains statistical relationship between asset volatility and returns.
method Uses multiplicative Langevin process with adjustable coherence time.
result Exactly equivalent to Inverse Gamma distribution for volatility.
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the evolution of wealth in a pure gambling process, where the entire sum of wealths of two agents is up for gambling, and randomly shared between the agents. For this equation the analytical form of the steady states is found for va…
The paper introduces a new stochastic volatility model with long-term memory and jumps.
problem Developing a model for variance and volatility swaps with long-term memory and jumps.
method Fractional Barndorff-Nielsen and Shephard model incorporating long-term memory and jumps.
result Arbitrage-free prices for variance and volatility swaps derived for the new model.
A new method calculates fractional moments using the moment-generating function.
problem Computing fractional moments from probability densities.
method Integral framework based on moment-generating function.
result Exact integral expressions for various types of moments.
Fourier methods fail to accurately approximate option Greeks in realistic market conditions.
problem Failure of Fourier pricing techniques to approximate Greeks in realistic market parameters.
method Used Fourier techniques like Carr-Madan formula, COS method, and Lewis formula to approximate Greeks, which failed in some market conditions.
result Empirically showed that Fourier methods completely fail to approximate Greeks in realistic market environments.
A novel Bayesian method for dynamic sparsity in Gaussian dynamic linear regression.
problem Variable selection and shrinkage in time-varying regression models.
method Time-varying sparsity via Markov switching priors for coefficients' variances, extending spike-and-slab priors.
result Induces smoothness or shrinkage towards zero at each time point, leading to improved model performance.
Modeling volatility with Chained Gamma Distributions for financial time series.
problem Volatility clustering in financial time series, especially in estimating temporal autocorrelation of logarithmic variance of returns.
method Dynamic Bayesian Network with conjugate prior relation of normal-gamma and gamma-gamma, using variational methods for quick approximate solutions.
result The model can express heavier tails than Gaussians, achieving positive excess kurtosis, and runs faster than Monte Carlo methods.
We discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades, and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown both through a variational approach based on the minimization of the Boltzmann e…
We unify and extend a number of approaches related to constructing multivariate Variance-Gamma (V.G.) models for option pricing. An overarching model is derived by subordinating multivariate Brownian motion to a subordinator from the Thorin (1977) class of generalised Gamma convolution subordinators. A class of models …
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by Lévy processes, extending earlier works which focused on the Black-Scholes and continuous stochastic volatility models. Usin…