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 “variance gamma++”
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.
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 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.
The weak variance-alpha-gamma process is a multivariate Lévy process constructed by weakly subordinating Brownian motion, possibly with correlated components with an alpha-gamma subordinator. It generalises the variance-alpha-gamma process of Semeraro constructed by traditional subordination. We compare three calibrati…
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.
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.
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).
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.
This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same firsts four cumulants. This approach is particularly convenient for pricing Americ…
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift, which makes it a time-changed Brownian motion. In general, the finite difference me…
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.
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.
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.
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…
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.
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.
This paper describes another extension of the Local Variance Gamma model originally proposed by P. Carr in 2008, and then further elaborated on by Carr and Nadtochiy, 2017 (CN2017), and Carr and Itkin, 2018 (CI2018). As compared with the latest version of the model developed in CI2018 and called the ELVG (the Expanded …
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.
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…
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributions, Negative binomial regression, Poisson-Gamma hierarchical models, …
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.
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.
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.
We establish several closed pricing formula for various path-independent payoffs, under an exponential Lévy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools from Mellin transform theory as well as from multidimensional complex analysis. Par…
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.
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…
The paper proposes an expanded version of the Local Variance Gamma model of Carr and Nadtochiy by adding drift to the governing underlying process. Still in this new model it is possible to derive an ordinary differential equation for the option price which plays a role of Dupire's equation for the standard local volat…
On Mean-Variance Analysisq-fin.PM
This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma approximation is employed to overcome it. Thus, the optimization problem is reduced to a we…
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.
We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- a…
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 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 …
A new method for computing Greeks without bias, improving stability.
problem Inaccurate and unstable computation of second order Greeks (like Gamma) in financial instruments.
method Apply Chebyshev interpolation techniques to finite differences for improved stability.
result Improved stability and accuracy in computing spot Greeks without bias.
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…
We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European options which are written in terms of the implied volatility are given. In particular…
The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment …
We illustrate how to compute local risk minimization (LRM) of call options for exponential Lévy models. We have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform method suggested by Carr & Madan. In particular, we consider Merton…
We discuss the difference between locally risk-minimizing and delta hedging strategies for exponential Lévy models, where delta hedging strategies in this paper are defined under the minimal martingale measure. We give firstly model-independent upper estimations for the difference. In addition we show numerical example…
The paper deals with learning probability distributions of observed data by artificial neural networks. We suggest a so-called gradient conjugate prior (GCP) update appropriate for neural networks, which is a modification of the classical Bayesian update for conjugate priors. We establish a connection between the gradi…
We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss correlation functions and leverage for three specific models -- multiplicative,…
We apply multilevel Monte Carlo for option pricing problems using exponential Lévy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate the computational efficiency of this approach. We derive estimates of the convergen…
Pricing joint claims on an asset and its realized variance under stochastic volatility modelsq-fin.PR
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims paying off at maturity a joint function of the underlying and its realised volatilit…
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.
Time-subordinated Brownian motion models improve financial market stochastic distribution.
problem Improving stochastic distribution modeling in financial markets.
method Fourier theory and methodology for time-subordinated Brownian motion models, extending real domain to complex plane.
result Characterization and direct study of stochastic time-change from full process.
This paper considers options pricing when the assumption of normality is replaced with that of the symmetry of the underlying distribution. Such a market affords many equivalent martingale measures (EMM). However we argue (as in the discrete-time setting of Klebaner and Landsman, 2007) that an EMM that keeps distributi…