Journal articles: 'Variance Gamma Model'

1

Carr, P., and A. Itkin. "Geometric Local Variance Gamma Model." Journal of Derivatives 27, no. 2 (September 11, 2019): 7–30. http://dx.doi.org/10.3905/jod.2019.1.084.

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Schoutens, Wim, and Geert Van Damme. "The β-variance gamma model." Review of Derivatives Research 14, no. 3 (July 24, 2010): 263–82. http://dx.doi.org/10.1007/s11147-010-9057-y.

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3

Fry, John, Oliver Smart, Jean-Philippe Serbera, and Bernhard Klar. "A Variance Gamma model for Rugby Union matches." Journal of Quantitative Analysis in Sports 17, no. 1 (May 5, 2020): 67–75. http://dx.doi.org/10.1515/jqas-2019-0088.

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Abstract Amid much recent interest we discuss a Variance Gamma model for Rugby Union matches (applications to other sports are possible). Our model emerges as a special case of the recently introduced Gamma Difference distribution though there is a rich history of applied work using the Variance Gamma distribution – particularly in finance. Restricting to this special case adds analytical tractability and computational ease. Our three-dimensional model extends classical two-dimensional Poisson models for soccer. Analytical results are obtained for match outcomes, total score and the awarding of bonus points. Model calibration is demonstrated using historical results, bookmakers’ data and tournament simulations.

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4

SEMERARO, PATRIZIA. "A MULTIVARIATE VARIANCE GAMMA MODEL FOR FINANCIAL APPLICATIONS." International Journal of Theoretical and Applied Finance 11, no. 01 (February 2008): 1–18. http://dx.doi.org/10.1142/s0219024908004701.

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In this paper we subordinate a multivariate Brownian motion with independent components by a multivariate gamma subordinator. The resulting process is a generalization of the bivariate variance gamma process proposed by Madan and Seneta [7], mentioned in Cont and Tankov [4] and calibrated in Luciano and Schoutens [5] as a price process. Our main contribution here is to introduce a multivariate subordinator with gamma margins. We investigate the process, determine its Lévy triplet and analyze its dependence structure. At the end we propose an exponential Lévy price model.

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5

Ivanov, Roman V. "On risk measuring in the variance-gamma model." Statistics & Risk Modeling 35, no. 1-2 (January 1, 2018): 23–33. http://dx.doi.org/10.1515/strm-2017-0008.

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AbstractIn this paper, we discuss the problem of calculating the primary risk measures in the variance-gamma model. A portfolio of investments in a one-period setting is considered. It is supposed that the investment returns are dependent on each other. In terms of the variance-gamma model, we assume that there are relations in both groups of the normal random variables and the gamma stochastic volatilities. The value at risk, the expected shortfall and the entropic monetary risk measures are discussed. The obtained analytical expressions are based on values of hypergeometric functions.

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6

Orzechowski, Arkadiusz. "PRICING EUROPEAN OPTIONS IN THE VARIANCE GAMMA MODEL." Metody Ilościowe w Badaniach Ekonomicznych 20, no. 1 (June 10, 2019): 45–53. http://dx.doi.org/10.22630/mibe.2019.20.1.5.

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7

Cheng, Min, and Yubo Li. "Convertible Bond Pricing Based on Variance Gamma Model." Saudi Journal of Economics and Finance 4, no. 6 (June 24, 2020): 287–92. http://dx.doi.org/10.36348/sjef.2020.v04i06.015.

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8

Seneta, Eugene. "Fitting the variance-gamma model to financial data." Journal of Applied Probability 41, A (2004): 177–87. http://dx.doi.org/10.1017/s0021900200112288.

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This paper has as its main theme the fitting in practice of the variance-gamma distribution, which allows for skewness, by moment methods. This fitting procedure allows for possible dependence of increments in log returns, while retaining their stationarity. It is intended as a step in a partial synthesis of some ideas of Madan, Carr and Chang (1998) and of Heyde (1999). Standard estimation and hypothesis-testing theory depends on a large sample of observations which are independently as well as identically distributed and consequently may give inappropriate conclusions in the presence of dependence.

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9

AGUILAR, JEAN-PHILIPPE. "SOME PRICING TOOLS FOR THE VARIANCE GAMMA MODEL." International Journal of Theoretical and Applied Finance 23, no. 04 (June 2020): 2050025. http://dx.doi.org/10.1142/s0219024920500259.

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We establish several closed pricing formulas 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. Particular focus is made on the symmetric process, but extension to the asymmetric process is also provided. Speed of convergence and comparison with numerical methods (Fourier transform, quadrature approximations, Monte Carlo simulations) are also discussed; notable feature is the accelerated convergence of the series for short-term options, which constitutes an interesting improvement of numerical Fourier inversion techniques.

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10

Seneta, Eugene. "Fitting the variance-gamma model to financial data." Journal of Applied Probability 41, A (2004): 177–87. http://dx.doi.org/10.1239/jap/1082552198.

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This paper has as its main theme the fitting in practice of the variance-gamma distribution, which allows for skewness, by moment methods. This fitting procedure allows for possible dependence of increments in log returns, while retaining their stationarity. It is intended as a step in a partial synthesis of some ideas of Madan, Carr and Chang (1998) and of Heyde (1999). Standard estimation and hypothesis-testing theory depends on a large sample of observations which are independently as well as identically distributed and consequently may give inappropriate conclusions in the presence of dependence.

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11

Finlay, Richard, and Eugene Seneta. "Stationary-increment Student and variance-gamma processes." Journal of Applied Probability 43, no. 02 (June 2006): 441–53. http://dx.doi.org/10.1017/s0021900200001741.

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A continuous-time model with stationary increments for asset price {P t } is an extension of the symmetric subordinator model of Heyde (1999), and allows for skewness of returns. In the setting of independent variance-gamma-distributed returns the model resembles closely that of Madan, Carr, and Chang (1998). A simple choice of parameters renders {e−rt P t } a familiar martingale. We then specify the activity time process, {T t }, for which {T t − t} is asymptotically self-similar and {τ t }, with τ t = T t − T t−1, is gamma distributed. This results in a skew variance-gamma distribution for each log price increment (return) X t and a model for {X t } which incorporates long-range dependence in squared returns. Our approach mirrors that for the (symmetric) Student process model of Heyde and Leonenko (2005), to which the present work is intended as a complement and a sequel. One intention is to compare, partly on the basis of fitting to data, versions of the general model wherein the returns have either (symmetric) t-distributions or variance-gamma distributions.

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12

Finlay, Richard, and Eugene Seneta. "Stationary-increment Student and variance-gamma processes." Journal of Applied Probability 43, no. 2 (June 2006): 441–53. http://dx.doi.org/10.1239/jap/1152413733.

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A continuous-time model with stationary increments for asset price {Pt} is an extension of the symmetric subordinator model of Heyde (1999), and allows for skewness of returns. In the setting of independent variance-gamma-distributed returns the model resembles closely that of Madan, Carr, and Chang (1998). A simple choice of parameters renders {e−rtPt} a familiar martingale. We then specify the activity time process, {Tt}, for which {Tt−t} is asymptotically self-similar and {τt}, with τt=Tt−Tt−1, is gamma distributed. This results in a skew variance-gamma distribution for each log price increment (return)Xtand a model for {Xt} which incorporates long-range dependence in squared returns. Our approach mirrors that for the (symmetric) Student process model of Heyde and Leonenko (2005), to which the present work is intended as a complement and a sequel. One intention is to compare, partly on the basis of fitting to data, versions of the general model wherein the returns have either (symmetric)t-distributions or variance-gamma distributions.

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13

Ngugi, AM, Eben Maré, and R. Kufakunesu. "Pricing variable annuity guarantees in South Africa under a Variance-Gamma model." South African Actuarial Journal 15, no. 1 (December 17, 2015): 131. http://dx.doi.org/10.4314/saaj.v15i1.6.

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14

Bishop, Craig H., and Elizabeth A. Satterfield. "Hidden Error Variance Theory. Part I: Exposition and Analytic Model." Monthly Weather Review 141, no. 5 (May 1, 2013): 1454–68. http://dx.doi.org/10.1175/mwr-d-12-00118.1.

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Abstract A conundrum of predictability research is that while the prediction of flow-dependent error distributions is one of its main foci, chaos fundamentally hides flow-dependent forecast error distributions from empirical observation. Empirical estimation of such error distributions requires a large sample of error realizations given the same flow-dependent conditions. However, chaotic elements of the flow and the observing network make it impossible to collect a large enough conditioned error sample to empirically define such distributions and their variance. Such conditional variances are “hidden.” Here, an exposition of the problem is developed from an ensemble Kalman filter data assimilation system applied to a 10-variable nonlinear chaotic model and 25 000 replicate models. The 25 000 replicates reveal the error variances that would otherwise be hidden. It is found that the inverse-gamma distribution accurately approximates the posterior distribution of conditional error variances given an imperfect ensemble variance and provides a reasonable approximation to the prior climatological distribution of conditional error variances. A new analytical model shows how the properties of a likelihood distribution of ensemble variances given a true conditional error variance determine the posterior distribution of error variances given an ensemble variance. The analytically generated distributions are shown to satisfactorily fit empirically determined distributions. The theoretical analysis yields a rigorous interpretation and justification of hybrid error variance models that linearly combine static and flow-dependent estimates of forecast error variance; in doing so, it also helps justify and inform hybrid error covariance models.

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15

Madan, Dilip B., and Eugene Seneta. "The Variance Gamma (V.G.) Model for Share Market Returns." Journal of Business 63, no. 4 (January 1990): 511. http://dx.doi.org/10.1086/296519.

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16

Fragiadakis, K., D. Karlis, and S. G. Meintanis. "Inference procedures for the variance gamma model and applications." Journal of Statistical Computation and Simulation 83, no. 3 (March 2013): 555–67. http://dx.doi.org/10.1080/00949655.2011.624518.

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17

Hoyyi, A., Tarno, D. A. I. Maruddani, and R. Rahmawati. "Variance gamma for stock model performance with excess kurtosis." Journal of Physics: Conference Series 1943, no. 1 (July 1, 2021): 012146. http://dx.doi.org/10.1088/1742-6596/1943/1/012146.

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18

Cadonna, Annalisa, Sylvia Frühwirth-Schnatter, and Peter Knaus. "Triple the Gamma—A Unifying Shrinkage Prior for Variance and Variable Selection in Sparse State Space and TVP Models." Econometrics 8, no. 2 (May 20, 2020): 20. http://dx.doi.org/10.3390/econometrics8020020.

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Time-varying parameter (TVP) models are very flexible in capturing gradual changes in the effect of explanatory variables on the outcome variable. However, in particular when the number of explanatory variables is large, there is a known risk of overfitting and poor predictive performance, since the effect of some explanatory variables is constant over time. We propose a new prior for variance shrinkage in TVP models, called triple gamma. The triple gamma prior encompasses a number of priors that have been suggested previously, such as the Bayesian Lasso, the double gamma prior and the Horseshoe prior. We present the desirable properties of such a prior and its relationship to Bayesian Model Averaging for variance selection. The features of the triple gamma prior are then illustrated in the context of time varying parameter vector autoregressive models, both for simulated dataset and for a series of macroeconomics variables in the Euro Area.

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19

Linders, Daniël, and Ben Stassen. "The multivariate Variance Gamma model: basket option pricing and calibration." Quantitative Finance 16, no. 4 (July 3, 2015): 555–72. http://dx.doi.org/10.1080/14697688.2015.1043934.

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20

Lam, K., E. Chang, and M. C. Lee. "An empirical test of the variance gamma option pricing model." Pacific-Basin Finance Journal 10, no. 3 (June 2002): 267–85. http://dx.doi.org/10.1016/s0927-538x(02)00047-1.

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21

ZHENG, Y. J., Z. H. YANG, and Y. C. HON. "MESHLESS COLLOCATION METHOD FOR OPTION PRICING BY VARIANCE GAMMA MODEL." International Journal of Computational Methods 10, no. 03 (April 17, 2013): 1350004. http://dx.doi.org/10.1142/s0219876213500047.

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Based on the use of radial basis functions (RBFs), we present in this paper a meshless collocation method to compute both European and American option prices by solving the variance gamma (VG) model. The valuation of the financial derivatives is performed by solving a corresponding partial integro-differential equation (PIDE). In the case of European option, numerical comparison with the analytical solution shows that the proposed scheme achieves a higher accurate approximation than most existing numerical methods. When analytical solution is not available in the case of American option, we use a dividend process to obtain an alternative characterization of the American option so that solution to the PIDE can be achieved in the entire computational region. Since the RBFs used in this paper are infinitely differentiable, the approximation of the derivatives of option prices can be obtained at no extra interpolation cost. In addition, the leave-one-out cross validation (LOOCV) algorithm is generalized for obtaining a local optimal choice of the shape parameter contained in the RBFs for superior convergence. Several numerical examples are given to verify the efficiency and stability of the proposed method.

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22

IVANOV, ROMAN V. "OPTION PRICING IN THE VARIANCE-GAMMA MODEL UNDER THE DRIFT JUMP." International Journal of Theoretical and Applied Finance 21, no. 04 (June 2018): 1850018. http://dx.doi.org/10.1142/s0219024918500188.

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This paper continues elements of the research direction of the work of Madan et al. [(1998) The variance gamma process and option pricing, European Finance Review 2, 79–105] and gives analytical expressions for the prices of digital and European call options in the variance-gamma model under the assumption that the linear drift rate of stock log-returns can suddenly jump downwards. The time of the jump is taken to be exponentially distributed. The formulas obtained require the computation of some generalized hyperbolic functions.

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23

Andersen, Per Kragh, John P. Klein, Kim M. Knudsen, and Rene Tabanera y Palacios. "Estimation of Variance in Cox's Regression Model with Shared Gamma Frailties." Biometrics 53, no. 4 (December 1997): 1475. http://dx.doi.org/10.2307/2533513.

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24

Rathgeber, Andreas W., Johannes Stadler, and Stefan Stöckl. "Modeling share returns - an empirical study on the Variance Gamma model." Journal of Economics and Finance 40, no. 4 (February 20, 2015): 653–82. http://dx.doi.org/10.1007/s12197-014-9306-2.

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25

Febrer, Pedro, and João Guerra. "Residue Sum Formula for Pricing Options under the Variance Gamma Model." Mathematics 9, no. 10 (May 18, 2021): 1143. http://dx.doi.org/10.3390/math9101143.

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We present and prove a triple sum series formula for the European call option price in a market model where the underlying asset price is driven by a Variance Gamma process. In order to obtain this formula, we present some concepts and properties of multidimensional complex analysis, with particular emphasis on the multidimensional Jordan Lemma and the application of residue calculus to a Mellin–Barnes integral representation in C3, for the call option price. Moreover, we derive triple sum series formulas for some of the Greeks associated to the call option and we discuss the numerical accuracy and convergence of the main pricing formula.

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26

Ribeiro, Claudia, and Nick Webber. "Valuing path-dependent options in the variance-gamma model by Monte Carlo with a gamma bridge." Journal of Computational Finance 7, no. 2 (2003): 81–100. http://dx.doi.org/10.21314/jcf.2003.110.

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27

Madan, Dilip B., Wim Schoutens, and King Wang. "Bilateral multiple gamma returns: Their risks and rewards." International Journal of Financial Engineering 07, no. 01 (March 2020): 2050008. http://dx.doi.org/10.1142/s2424786320500085.

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The bilateral gamma model for returns is naturally derived from the lognormal model. Maximizing entropy in a random time change delivers the symmetric variance gamma model. The asymmetric variance gamma follows on incorporating skewness. Differential speeds for the upward and downward motions lead to the bilateral gamma. A further generalizations results in the bilateral double gamma model when the speed parameter of the bilateral gamma model is itself taken to be gamma distributed on entropy maximization. A rich five to seven parameter specification of preferences renders possible the extraction of physical densities from option prices. The quality of such extraction is measured by examining the uniformity of the estimated distribution functions evaluated at realized forward returns. The economic value of risky returns is seen to embed three/five risk premia for the bilateral gamma/bilateral double gamma. For the bilateral gamma they are up and down side volatilities compensated in up and down side drifts, and the down side drift compensated in the up side drift. For the bilateral double gamma one adds in addition compensations for skewness. Results reveal a drop in the down side risk premium since the crisis with an increase in the recent period.

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28

FINLAY, RICHARD, and EUGENE SENETA. "OPTION PRICING WITH VG–LIKE MODELS." International Journal of Theoretical and Applied Finance 11, no. 08 (December 2008): 943–55. http://dx.doi.org/10.1142/s0219024908005093.

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We relax separately two assumptions regarding the Variance Gamma (VG) process and price options accordingly. In the case of the Difference of Gammas model we achieve a better fit to market data than achieved by other comparable models. In the case of the long range dependent VG model, we find that the current "skew-correcting" approach to pricing options has shortcomings, and identify a number of model characteristics (flexible skewness, dependence of squared returns, accommodation of the leverage effect) which appear to be important in achieving a good fit to market data.

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29

Loregian, Angela, Lorenzo Mercuri, and Edit Rroji. "Approximation of the variance gamma model with a finite mixture of normals." Statistics & Probability Letters 82, no. 2 (February 2012): 217–24. http://dx.doi.org/10.1016/j.spl.2011.10.004.

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30

Daal, Elton A., and Dilip B. Madan. "An Empirical Examination of the Variance‐Gamma Model for Foreign Currency Options*." Journal of Business 78, no. 6 (November 2005): 2121–52. http://dx.doi.org/10.1086/497039.

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31

Mayo, Anita. "On the numerical evaluation of option prices in the variance gamma model." International Journal of Computer Mathematics 86, no. 2 (February 2009): 251–60. http://dx.doi.org/10.1080/00207160701874813.

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32

KAO, LIE-JANE. "LOCALLY RISK-NEUTRAL VALUATION OF OPTIONS IN GARCH MODELS BASED ON VARIANCE-GAMMA PROCESS." International Journal of Theoretical and Applied Finance 15, no. 02 (March 2012): 1250015. http://dx.doi.org/10.1142/s021902491250015x.

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This study develops a GARCH-type model, i.e., the variance-gamma GARCH (VG GARCH) model, based on the two major strands of option pricing literature. The first strand of the literature uses the variance-gamma process, a time-changed Brownian motion, to model the underlying asset price process such that the possible skewness and excess kurtosis on the distributions of asset returns are considered. The second strand of the literature considers the propagation of the previously arrived news by including the feedback and leverage effects on price movement volatility in a GARCH framework. The proposed VG GARCH model is shown to obey a locally risk-neutral valuation relationship (LRNVR) under the sufficient conditions postulated by Duan (1995). This new model provides a unified framework for estimating the historical and risk-neutral distributions, and thus facilitates option pricing calibration using historical underlying asset prices. An empirical study is performed comparing the proposed VG GARCH model with four competing pricing models: benchmark Black–Scholes, ad hoc Black–Scholes, normal NGARCH, and stochastic volatility VG. The performance of the VG GARCH model versus these four competing models is then demonstrated.

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33

Kemda, Lionel Establet, Chun-Kai Huang, and Knowledge Chinhamu. "Value-at-risk for the USD/ZAR exchange rate: The Variance-Gamma model." South African Journal of Economic and Management Sciences 18, no. 4 (November 27, 2015): 551–66. http://dx.doi.org/10.4102/sajems.v18i4.966.

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A country’s level of exchange risk is closely linked to its financial stability, on a macro-economic scale. South African exchange rates, in particular, have a significant impact on imports, inflation, consumer prices and monetary policies. Consequently, it is imperative for economists and investors to assess accurately the associated exchange risks. Exchange rates, like most financial time series, are leptokurtic and contradict the classical Gaussian assumption. We therefore introduce subclasses of the generalised hyperbolic distribution as alternative models and contrast these with the normal distribution. We conclude that the variance-gamma model is the most robust for describing the log-returns of daily USD/ZAR exchange rates and their related Value-at-Risk (VaR) estimates. The model selection methodologies utilised in our analyses include the robust Kolmogorov-Smirnov test and the Akaike information criterion. Backtesting on the adequacy of VaR estimates is also performed using the Kupiec likelihood ratio test.

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34

RUJIVAN, SANAE. "A NOVEL ANALYTICAL APPROACH FOR PRICING DISCRETELY SAMPLED GAMMA SWAPS IN THE HESTON MODEL." ANZIAM Journal 57, no. 3 (January 2016): 244–68. http://dx.doi.org/10.1017/s1446181115000309.

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The main purpose of this paper is to present a novel analytical approach for pricing discretely sampled gamma swaps, defined in terms of weighted variance swaps of the underlying asset, based on Heston’s two-factor stochastic volatility model. The closed-form formula obtained in this paper is in a much simpler form than those proposed in the literature, which substantially reduces the computational burden and can be implemented efficiently. The solution procedure presented in this paper can be adopted to derive closed-form solutions for pricing various types of weighted variance swaps, such as self-quantoed variance and entropy swaps. Most interestingly, we discuss the validity of the current solutions in the parameter space, and provide market practitioners with some remarks for trading these types of weighted variance swaps.

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35

Haskard, K. A., B. G. Rawlins, and R. M. Lark. "A linear mixed model, with non-stationary mean and covariance, for soil potassium based on gamma radiometry." Biogeosciences 7, no. 7 (July 2, 2010): 2081–89. http://dx.doi.org/10.5194/bg-7-2081-2010.

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Abstract. In this paper we present a linear mixed model for the potassium content of soil across a large region of eastern England in which the mean is modelled as a linear function of the passive gamma-ray emissions of the earth surface in the energy interval commonly associated with potassium decay. Non-stationary models are proposed for the random effect, which is the variation not captured by this regression. Specifically, we assume that the local spectrum of the standardized random effect can be obtained by tempering a common (stationary) spectrum, that is to say raising its values to a power, the tempering parameter, which is itself modelled as a linear function of the radiometric data. This allows the "smoothness" of the random effect to vary locally. In addition the local spatially correlated variance and "nugget" variance (apparently uncorrelated given the resolution of the sampling) can also be modelled as a function of the radiometric data. Using the radiometric signal as a covariate gave some improvement in the precision of predictions of soil potassium at validation sites. In addition, there was evidence that non-stationary models for the random effect fitted the data better than stationary models, and this difference was statistically significant. Non-stationary models also appeared to describe the error variance of predictions at the validation sites better. Further work is needed on selection among alternative non-stationary models, since simple procedures used here, based on comparing log-likelihood ratios of nested models and the Akaike information criterion for non-nested models, did not identify the model which gave the best account of the prediction error variances at validation sites.

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Haskard, K. A., B. G. Rawlins, and R. M. Lark. "A linear mixed model, with non-stationary mean and covariance, for soil potassium based on gamma radiometry." Biogeosciences Discussions 7, no. 2 (March 16, 2010): 1839–62. http://dx.doi.org/10.5194/bgd-7-1839-2010.

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Abstract. In this paper we present a linear mixed model for the potassium content of soil across a large region of eastern England in which the mean is modelled as a linear function of the passive gamma-ray emissions of the earth surface in the energy interval commonly associated with potassium decay. Non-stationary models are proposed for the random effect, the variation not captured by this regression. Specifically, we assume that the local spectrum of the standardized random effect can be obtained by tempering a common (stationary) spectrum, that is to say raising its values to a power, the tempering parameter, which is itself modelled as a linear function of the radiometric data. This allows the "smoothness" of the random effect to vary locally. In addition the local spatially correlated variance and "nugget" variance (apparently uncorrelated given the resolution of the sampling) can also be modelled as a function of the radiometric data. Using the radiometric signal as a covariate gave some improvement in the precision of predictions of soil potassium at validation sites. In addition, there was evidence that non-stationary models for the random effect fitted the data better than stationary models, and this difference was statistically significant. Non-stationary models also appeared to describe the error variance of predictions at the validation sites better. Further work is needed on selection among alternative non-stationary models, since simple procedures used here, based on comparing log-likelihood ratios of nested models and the Akaike information criterion for non-nested models, did not identify the model which gave the best account of the prediction error variances at validation sites.

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37

Bernis, Guillaume, Riccardo Brignone, Simone Scotti, and Carlo Sgarra. "A Gamma Ornstein–Uhlenbeck model driven by a Hawkes process." Mathematics and Financial Economics 15, no. 4 (March 24, 2021): 747–73. http://dx.doi.org/10.1007/s11579-021-00295-0.

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AbstractWe propose an extension of the $$\Gamma $$ Γ -OU Barndorff-Nielsen and Shephard model taking into account jump clustering phenomena. We assume that the intensity process of the Hawkes driver coincides, up to a constant, with the variance process. By applying the theory of continuous-state branching processes with immigration, we prove existence and uniqueness of strong solutions of the SDE governing the asset price dynamics. We propose a measure change of self-exciting Esscher type in order to describe the relation between the risk-neutral and the historical dynamics, showing that the $$\Gamma $$ Γ -OU Hawkes framework is stable under this probability change. By exploiting the affine features of the model we provide an explicit form for the Laplace transform of the asset log-return, for its quadratic variation and for the ergodic distribution of the variance process. We show that the proposed model exhibits a larger flexibility in comparison with the $$\Gamma $$ Γ -OU model, in spite of the same number of parameters required. We calibrate the model on market vanilla option prices via characteristic function inversion techniques, we study the price sensitivities and propose an exact simulation scheme. The main financial achievement is that implied volatility of options written on VIX is upward shaped due to the self-exciting property of Hawkes processes, in contrast with the usual downward slope exhibited by the $$\Gamma $$ Γ -OU Barndorff-Nielsen and Shephard model.

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38

Göncü, Ahmet, Mehmet Oğuz Karahan, and Tolga Umut Kuzubaş. "Fitting the Variance-Gamma Model: A Goodness-of-Fit Check for Emerging Markets." Bogazici Journal 27, no. 2 (July 1, 2013): 1–10. http://dx.doi.org/10.21773/boun.27.2.1.

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39

Lionel Establet, Kemda,, Huang, Chun-Kai, and Chinhamu, Knowledge. "Value-at-risk for the USD/ZAR exchange rate : the variance-gamma model." South African Journal of Economic and Management Sciences 18, no. 4 (2015): 551–56. http://dx.doi.org/10.17159/2222-3436/2015/v18n4a8.

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40

Nitithumbundit, Thanakorn, and Jennifer S. K. Chan. "ECM Algorithm for Auto-Regressive Multivariate Skewed Variance Gamma Model with Unbounded Density." Methodology and Computing in Applied Probability 22, no. 3 (December 23, 2019): 1169–91. http://dx.doi.org/10.1007/s11009-019-09762-0.

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41

Dzupire, Nelson Christopher, Philip Ngare, and Leo Odongo. "A Poisson-Gamma Model for Zero Inflated Rainfall Data." Journal of Probability and Statistics 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/1012647.

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Rainfall modeling is significant for prediction and forecasting purposes in agriculture, weather derivatives, hydrology, and risk and disaster preparedness. Normally two models are used to model the rainfall process as a chain dependent process representing the occurrence and intensity of rainfall. Such two models help in understanding the physical features and dynamics of rainfall process. However rainfall data is zero inflated and exhibits overdispersion which is always underestimated by such models. In this study we have modeled the two processes simultaneously as a compound Poisson process. The rainfall events are modeled as a Poisson process while the intensity of each rainfall event is Gamma distributed. We minimize overdispersion by introducing the dispersion parameter in the model implemented through Tweedie distributions. Simulated rainfall data from the model shows a resemblance of the actual rainfall data in terms of seasonal variation, means, variance, and magnitude. The model also provides mechanisms for small but important properties of the rainfall process. The model developed can be used in forecasting and predicting rainfall amounts and occurrences which is important in weather derivatives, agriculture, hydrology, and prediction of drought and flood occurrences.

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Pourreza, Hormatollah, Ezzatallah Baloui Jamkhaneh, and Einolah Deiri. "A family of Gamma-generated distributions: Statistical properties and applications." Statistical Methods in Medical Research 30, no. 8 (May 18, 2021): 1850–73. http://dx.doi.org/10.1177/09622802211009262.

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In this paper, we concentrate on the statistical properties of Gamma-X family of distributions. A special case of this family is the Gamma-Weibull distribution. Therefore, the statistical properties of Gamma-Weibull distribution as a sub-model of Gamma-X family are discussed such as moments, variance, skewness, kurtosis and Rényi entropy. Also, the parameters of the Gamma-Weibull distribution are estimated by the method of maximum likelihood. Some sub-models of the Gamma-X are investigated, including the cumulative distribution, probability density, survival and hazard functions. The Monte Carlo simulation study is conducted to assess the performances of these estimators. Finally, the adequacy of Gamma-Weibull distribution in data modeling is verified by the two clinical real data sets. Mathematics Subject Classification: 62E99; 62E15

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Mozumder, Sharif, Ghulam Sorwar, and Kevin Dowd. "Revisiting variance gamma pricing: An application to S&P500 index options." International Journal of Financial Engineering 02, no. 02 (June 2015): 1550022. http://dx.doi.org/10.1142/s242478631550022x.

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This paper reformulates the Lévy–Kintchine formula to make it suitable for modeling the stochastic time-changing effects of Lévy processes. Using the variance gamma (VG) process as an example, it illustrates the dynamic properties of a Lévy process and revisits the earlier work of Geman (2002). It also shows how the model can be calibrated to price options under a Lévy VG process, and calibrates the model on recent S&P500 index options data. It then compares the pricing performance of fast Fourier transform (FFT) and fractional Fourier transform (FRFT) approaches to model calibration and investigates the trade-off between calibration performance and required calculation time.

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ARAI, TAKUJI, YUTO IMAI, and RYOICHI SUZUKI. "NUMERICAL ANALYSIS ON LOCAL RISK-MINIMIZATION FOR EXPONENTIAL LÉVY MODELS." International Journal of Theoretical and Applied Finance 19, no. 02 (March 2016): 1650008. http://dx.doi.org/10.1142/s0219024916500084.

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We illustrate how to compute local risk minimization (LRM) of call options for exponential Lévy models. Here, LRM is a popular hedging method through a quadratic criterion for contingent claims in incomplete markets. Arai & Suzuki (2015) 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 (FFT) method suggested by by Carr & Madan (1999). Considering Merton jump-diffusion models and variance gamma models as typical examples of exponential Lévy models, we provide the forms for the FFT explicitly; and compute the values of LRM numerically for given parameter sets. Furthermore, we illustrate numerical results for a variance gamma model with estimated parameters from the Nikkei 225 index.

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Finlay, Richard, and Eugene Seneta. "A Gamma Activity Time Process with Noninteger Parameter and Self-Similar Limit." Journal of Applied Probability 44, no. 04 (December 2007): 950–59. http://dx.doi.org/10.1017/s002190020000365x.

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We construct a process with gamma increments, which has a given convex autocorrelation function and asymptotically a self-similar limit. This construction validates the use of long-range dependent t and variance-gamma subordinator models for actual financial data as advocated in Heyde and Leonenko (2005) and Finlay and Seneta (2006), in that it allows for noninteger-valued model parameters to occur as found empirically by data fitting.

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Finlay, Richard, and Eugene Seneta. "A Gamma Activity Time Process with Noninteger Parameter and Self-Similar Limit." Journal of Applied Probability 44, no. 4 (December 2007): 950–59. http://dx.doi.org/10.1239/jap/1197908816.

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We construct a process with gamma increments, which has a given convex autocorrelation function and asymptotically a self-similar limit. This construction validates the use of long-range dependent t and variance-gamma subordinator models for actual financial data as advocated in Heyde and Leonenko (2005) and Finlay and Seneta (2006), in that it allows for noninteger-valued model parameters to occur as found empirically by data fitting.

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Avramidis, Athanassios N., and Pierre L’Ecuyer. "Efficient Monte Carlo and Quasi–Monte Carlo Option Pricing Under the Variance Gamma Model." Management Science 52, no. 12 (December 2006): 1930–44. http://dx.doi.org/10.1287/mnsc.1060.0575.

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Chairunnnisa, Ubudia Hiliaily, Abdul Hoyyi, and Hasbi Yasin. "PEMODELAN TRANSFORMASI FAST-FOURIER PADA VALUASI OBLIGASI KORPORASI (Studi Kasus: PT. Bank Danamon Tbk, PT. Bank CIMB Niaga Tbk, dan PT. Bank UOB Indonesia Tbk)." Jurnal Gaussian 10, no. 1 (February 28, 2021): 85–93. http://dx.doi.org/10.14710/j.gauss.v10i1.30937.

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The basic assumption that is often used in bond valuations is the assumption on the Black-Scholes model. The practical assumption of the Black-Scholes model is the return of assets with normal distribution, but in reality there are many conditions where the return of assets of a company is not normally distributed and causing improperly developed bond valuation modeling. The Fast-Fourier Transform model (FFT) was developed as a solution to this problem. The Fast-Fourier Transformation Model is a Fourier transformation technique with high accuracy and is more effective because it uses characteristic functions. In this research, a modeling will be carried out to calculate bond valuations designed to take advantage of the computational power of the FFT. The characteristic function used is the Variance Gamma, which has the advantage of being able to capture data return behavior that is not normally distributed. The data used in this study are Sustainable Bonds I of Bank Danamon Phase I Year 2019 Series B, Sustainable Bonds II of Bank CIMB Niaga II Phase IV Year 2018 Series C, Sustainable Subordinated Bonds II of Bank UOB Indonesia Phase II 2019. The results obtained are FFT model using the Variance Gamma characteristic function gives more precise results for the return of assets with not normal distribution. Keywords: Bonds, Bond Valuation, Black-Scholes, Fast-Fourier Transform, Variance Gamma

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Smith, Valerie A., and John S. Preisser. "A marginalized two-part model with heterogeneous variance for semicontinuous data." Statistical Methods in Medical Research 28, no. 5 (February 16, 2018): 1412–26. http://dx.doi.org/10.1177/0962280218758358.

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Semicontinuous data, characterized by a point mass at zero followed by a positive, continuous distribution, arise frequently in medical research. These data are typically analyzed using two-part mixtures that separately model the probability of incurring a positive outcome and the distribution of positive values among those who incur them. In such a conditional specification, however, standard two-part models do not provide a marginal interpretation of covariate effects on the overall population. We have previously proposed a marginalized two-part model that yields more interpretable effect estimates by parameterizing the model in terms of the marginal mean. In the original formulation, a constant variance was assumed for the positive values. We now extend this model to a more general framework by allowing non-constant variance to be explicitly modeled as a function of covariates, and incorporate this variance into two flexible distributional assumptions, log-skew-normal and generalized gamma, both of which take the log-normal distribution as a special case. Using simulation studies, we compare the performance of each of these models with respect to bias, coverage, and efficiency. We illustrate the proposed modeling framework by evaluating the effect of a behavioral weight loss intervention on health care expenditures in the Veterans Affairs health system.

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Kittisuwan, Pichid. "Image Denoising via Bayesian Estimation of Statistical Parameter Using Generalized Gamma Density Prior in Gaussian Noise Model." Fluctuation and Noise Letters 14, no. 02 (May 4, 2015): 1550017. http://dx.doi.org/10.1142/s0219477515500170.

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The application of image processing in industry has shown remarkable success over the last decade, for example, in security and telecommunication systems. The denoising of natural image corrupted by Gaussian noise is a classical problem in image processing. So, image denoising is an indispensable step during image processing. This paper is concerned with dual-tree complex wavelet-based image denoising using Bayesian techniques. One of the cruxes of the Bayesian image denoising algorithms is to estimate the statistical parameter of the image. Here, we employ maximum a posteriori (MAP) estimation to calculate local observed variance with generalized Gamma density prior for local observed variance and Laplacian or Gaussian distribution for noisy wavelet coefficients. Evidently, our selection of prior distribution is motivated by efficient and flexible properties of generalized Gamma density. The experimental results show that the proposed method yields good denoising results.

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Journal articles on the topic 'Variance Gamma Model'

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