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Local variance gamma revisited

The Journal of Computational Finance, 2015
In this paper we develop a new method for implied volatility surface construction for FX options. The methodology is based on the local variance gamma model developed by Carr (2008). Our approach is to solve a simplified "one-step" version of the Dupire equation analytically under the assumption of a continuous five parameter diffusion function.
Markus Falck   +1 more
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The Variance Gamma Process and Option Pricing

Review of Finance, 1998
Abstract A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. Theprocess is obtained by evaluating Brownian motion with drift at a random time given by a gamma process.
Carr, P, Madan, DB, Chang, EC
openaire   +4 more sources

A Singular Gamma Variance Expansion

Wilmott, 2023
We give an analytical expansion for option prices and Black implied volatilities consistent with the Variance Gamma model [MCC98] based on a singular expansion of the standard gamma density in terms of the Dirac functions and its derivatives
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A MULTIVARIATE VARIANCE GAMMA MODEL FOR FINANCIAL APPLICATIONS [PDF]

open access: possibleInternational Journal of Theoretical and Applied Finance, 2008
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.
openaire   +3 more sources

Minimum Variance Unbiased Estimation in the Gamma Distribution

Communications in Statistics - Simulation and Computation, 1975
In this paper a new infinite series UMVU etimator far general functions of the scale parameter in the gamma distribution wita shape parameter known is presented. The formula gives is easy to employ,and also leads to simple approximations to the UMVU. These approximations are shown to perform well is the examples considered.
Woodward, W. A., Gray, H. L.
openaire   +2 more sources

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