On the numerical evaluation of option prices in the variance gamma model

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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Time for a Change: The Variance Gamma Model and Option Pricing

SSRN Electronic Journal ◽

10.2139/ssrn.956625 ◽

2005 ◽

Author(s):

Harvey J. Stein ◽

Peter P. Carr ◽

Apollo Hogan

Keyword(s):

Option Pricing ◽

Gamma Model ◽

Variance Gamma ◽

Variance Gamma Model

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A Variance Gamma model for Rugby Union matches

Journal of Quantitative Analysis in Sports ◽

10.1515/jqas-2019-0088 ◽

2020 ◽

Vol 17 (1) ◽

pp. 67-75

Author(s):

John Fry ◽

Oliver Smart ◽

Jean-Philippe Serbera ◽

Bernhard Klar

Keyword(s):

Three Dimensional ◽

Rugby Union ◽

Three Dimensional Model ◽

Gamma Model ◽

Variance Gamma ◽

Poisson Models ◽

History Of ◽

Bonus Points ◽

Variance Gamma Model ◽

Special Case

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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Stochastic Volatility II: Variance Gamma Model: Analysis and Implementation

SSRN Electronic Journal ◽

10.2139/ssrn.1579923 ◽

2010 ◽

Author(s):

Thomas Domenig ◽

Paolo Vanini

Keyword(s):

Stochastic Volatility ◽

Model Analysis ◽

Gamma Model ◽

Variance Gamma ◽

Variance Gamma Model

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On risk measuring in the variance-gamma model

Statistics & Risk Modeling ◽

10.1515/strm-2017-0008 ◽

2018 ◽

Vol 35 (1-2) ◽

pp. 23-33 ◽

Cited By ~ 3

Author(s):

Roman V. Ivanov

Keyword(s):

Value At Risk ◽

Hypergeometric Functions ◽

Risk Measures ◽

Random Variables ◽

Gamma Model ◽

Variance Gamma ◽

Stochastic Volatilities ◽

Investment Returns ◽

Variance Gamma Model ◽

Analytical Expressions

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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