In this work, we study the value of an Asian option in the case of exponential Levy markets. More specifically, we are interested in the NIG (normal inverse Gaussian) the VG (variance gamma) models. The exponential Levy models produce incomplete markets. There are therefore an infinite number of equivalent martingale m…
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48 results for “Exponential NIG model”
Closed-form formulas for path-independent options in a specific Lévy model.
problem Valuation of path-independent options in the exponential NIG model.
method Closed-form pricing formulas derived using a factorized representation in Mellin space and complex analysis.
result Valid closed-form formulas with quickly convergent series for various options.
In this paper we propose a transform method to compute the prices and greeks of barrier options driven by a class of Levy processes. We derive analytical expressions for the Laplace transforms in time of the prices and sensitivities of single barrier options in an exponential Levy model with hyper-exponential jumps. In…
Clustering of non-Gaussian data by variational Bayes for normal inverse Gaussian mixture modelsstat.ML
Improved VB algorithm for NIG mixtures outperforms Gaussian mixtures for non-Gaussian data.
problem Clustering non-Gaussian data, especially heavy-tailed and asymmetric.
method Proposed an improved VB algorithm for NIG mixture models and extended Dirichlet process mixture models.
result Outperforms Gaussian mixtures and existing NIG mixture models, especially for highly non-normative data.
A new model forecasts Value-at-Risk using NIG distribution and dynamic scores.
problem Forecasting Value-at-Risk (VaR) in financial markets.
method Proposes a parametric forecasting model based on the normal inverse Gaussian distribution (NIG) incorporating intraday information.
result The model outperforms traditional GARCH models, especially in high-risk scenarios.
The NIG model outperforms others in pricing S&P 500 index options.
problem Analyzing and pricing S&P 500 index options with Lévy jumps.
method Parameter estimation using SSE method for various models (BS, SV, SVJ, non-IID, Lévy (GH, NIG, CGMY)).
result NIG model outperforms other models in both in-sample and out-of-sample periods.
Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are considered. The use of variational Bayes approximations here is a substantial departure fr…
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…
We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at fixed dates. Our approach yields unbiased estimators with standard deviation in expected time for a variety of processes including the Black-Scholes model, Merton's jump-diffusion mod…
In this paper, an application of three GARCH-type models (sGARCH, iGARCH, and tGARCH) with Student t-distribution, Generalized Error distribution (GED), and Normal Inverse Gaussian (NIG) distribution are examined. The new development allows for the modeling of volatility clustering effects, the leptokurtic and the skew…
Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic modelsq-fin.PR
In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-diffusion mode…
The paper integrates behavioral distortions into portfolio optimization using implied probability weighting functions.
problem Behavioral distortions in probability weighting affect portfolio optimization under different return distributions.
method Developed a unified framework to extract probability weighting functions from optimal portfolios modeled under Gaussian and NIG distributions.
result Increasing tail fatness amplifies behavioral distortions, and shifts in risk-free rates alter the curvature of these distortions.
We introduce a wavelet-domain functional analysis of variance (fANOVA) method based on a Bayesian hierarchical model. The factor effects are modeled through a spike-and-slab mixture at each location-scale combination along with a normal-inverse-Gamma (NIG) conjugate setup for the coefficients and errors. A graphical mo…
Proposes a simpler method for quantifying uncertainty in time-series with volatility clustering.
problem Uncertainty quantification for time-series with volatility clustering.
method Proposes a Scale Mixture Distribution to quantify return forecast uncertainty in neural networks.
result The proposed method provides a favorable complexity-accuracy trade-off and separates model parameters into subnetworks.
We provide an integral representation for the (implied) copulas of dependent random variables in terms of their moment generating functions. The proof uses ideas from Fourier methods for option pricing. This representation can be used for a large class of models from mathematical finance, including Lévy and affine proc…
Computed tomography (CT) equivalent information is needed for attenuation correction in PET imaging and for dose planning in radiotherapy. Prior work has shown that Gaussian mixture models can be used to generate a substitute CT (s-CT) image from a specific set of MRI modalities. This work introduces a more flexible cl…
One popular approach to option pricing in Lévy models is through solving the related partial integro differential equation (PIDE). For the numerical solution of such equations powerful Galerkin methods have been put forward e.g. by Hilber et al. (2013). As in practice large classes of models are maintained simultaneous…
In this paper we present an application of the use of autocopulas for modelling financial time series showing serial dependencies that are not necessarily linear. The approach presented here is semi-parametric in that it is characterized by a non-parametric autocopula and parametric marginals. One advantage of using au…
We introduce a simple model for equity index derivatives. The model generalizes well known Lèvy Normal Tempered Stable processes (e.g. NIG and VG) with time dependent parameters. It accurately fits Equity index implied volatility surfaces in the whole time range of quoted instruments, including small time horizon (few …
Quantum computing speeds up option pricing for multiple assets.
problem High-dimensional integration bottleneck in option pricing.
method Calibrated marginal distributions, Gaussian copula, QAMC with QAE.
result QAMC reduces integration queries by 10-100 times for similar precision.
Extends option pricing framework without risk-free asset using Levy jumps.
problem Valuing derivatives in markets without a traded risk-free bond.
method Introduces common Levy jump dynamics, uses Ito-Levy calculus, FFT, and COS algorithms.
result Calibrations show jump models reduce pricing errors and fit volatility smiles better than Black-Scholes.
On spatially irregular ordinary differential equations and a pathwise volatility modelling frameworkq-fin.MF
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's squared volatility, or `cumulative variance'. In the new framework, corresponding p…
Incorporates matrix exponential into generative flows for improved performance.
problem Improving generative flow models for better density estimation.
method Integrates matrix exponential into generative flows, proposing new layers and modifying network architecture.
result The proposed model achieves great performance on density estimation.
New linear flows using exponential of linear transformations improve generative models.
problem Improving generative models in machine learning.
method Developed convolution exponentials and generalized Sylvester Flows using the exponential of linear transformations.
result Convolution exponentials and Convolutional Sylvester Flows outperform other models in log-likelihood.
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.
In a Markovian stochastic volatility model, we consider financial agents whose investment criteria are modelled by forward exponential performance processes. The problem of contingent claim indifference valuation is first addressed and a number of properties are proved and discussed. Special attention is given to the c…
We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks …
Quantum computing speeds up asset pricing models exponentially.
problem Solving dynamic nonlinear asset pricing models efficiently.
method Utilizes quantum superposition and entanglement to solve models exponentially faster than classical methods.
result Exponential computational speed-up for solving asset pricing models.
We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-para…
Motivated by the pricing of lookback options in exponential Lévy models, we study the difference between the continuous and discrete supremum of Lévy processes. In particular, we extend the results of Broadie et al. (1999) to jump-diffusion models. We also derive bounds for general exponential Lévy models.
In this paper, we propose the exponential Levy neural network (ELNN) for option pricing, which is a new non-parametric exponential Levy model using artificial neural networks (ANN). The ELNN fully integrates the ANNs with the exponential Levy model, a conventional pricing model. So, the ELNN can improve ANN-based model…
Exponentially smoothed RNNs improve industrial forecasting.
problem Complexity and non-stationarity in industrial time series data.
method Exponential smoothed recurrent neural networks (RNNs) for modeling non-linear dynamics.
result Exponentially smoothed RNNs outperform traditional models in multi-step forecasting.
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…
Exponential distribution is ubiquitous in the framework of multi-agent systems. An alternative approach with an economic motivation to derive the exponential distribution in the framework of iterations in the space of distributions is disclosed.
Efficient method for learning continuous exponential families beyond Gaussian.
problem Learning continuous exponential families with unbounded support.
method Interaction Screening approach for scalable learning of continuous graphical models.
result Our estimator maintains similar accuracy and sample complexity scalings compared to alternative approaches, while improving run-time.
On the Geometry of Discrete Exponential Families with Application to Exponential Random Graph Modelsstat.ML
There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with difficulties in computing maximum likelihood estimates. The issues associated with these difficulties relate to the bro…
Randomisation and recursion methods for mixed-exponential Levy models, with financial applicationsmath.PR
We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first-passage time probability and expected occupation time of sets of a Le…
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly…
The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity pattern of the optimal parameter. This work characterizes a certain strong conve…
We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models [Yang et al. 2015] did not allow positive dependencies for the exponential and Poisson generalizat…
An Auto-Regressive Formulation for Smoothing and Moving Mean with Exponentially Tapered Windowscs.LG
Auto-regressive models improve smoothing efficiency with exponentially tapered windows.
problem Improving time-series smoothing efficiency.
method An auto-regressive formulation for time-series smoothing.
result Auto-regressive models result in moving means with exponentially tapered windows.
EFDA extends LDA to non-Gaussian models using exponential families.
problem Classifying non-Gaussian data with LDA's limitations.
method EFDA uses exponential families to derive closed-form estimators for natural parameters and a linear decision rule.
result EFDA matches LDA's accuracy while reducing ECE by 2-6x, proving asymptotic calibration and efficiency.
SMRL uses score matching for efficient RL with exponential family models.
problem Efficient reinforcement learning with unknown transition models.
method Score matching for parameter estimation of exponential family models.
result Achieves online regret of .
In the setting of exponential investors and uncertainty governed by Brownian motions we first prove the existence of an incomplete equilibrium for a general class of models. We then introduce a tractable class of exponential-quadratic models and prove that the corresponding incomplete equilibrium is characterized by a …
Exponential functionals of Brownian motion have been extensively studied in financial and insurance mathematics due to their broad applications, for example, in the pricing of Asian options. The Black-Scholes model is appealing because of mathematical tractability, yet empirical evidence shows that geometric Brownian m…
A new method for exponentially weighted moving models using approximations.
problem Efficiently updating moving averages for time series data.
method Approximates EWMM using a fixed window and quadratic term, solving non-growing problems.
result Approximation produces estimates similar to exact EWMM.
Improved Gibbs sampler speeds up Bayesian exponential smoothing model.
problem Computational inefficiency of original NUTS sampler.
method Modifications to the original model and a bespoke Gibbs sampler.
result Significant improvement in sampling time by an order of magnitude.
CDEFs reduce model complexity and uncover time correlations.
problem Model complexity and data efficiency in probabilistic modeling.
method Builds on deep exponential families, ties weights for reduced parameters.
result CDEFs uncover time correlations with fewer parameters.