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The Risk Measurement under the Variance-Gamma Process with Drift Switching

Author

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  • Roman V. Ivanov

    (Laboratory of Control under Incomplete Information, V.A. Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya 65, 117997 Moscow, Russia)

Abstract

The paper discusses an extension of the variance-gamma process with stochastic linear drift coefficient. It is assumed that the linear drift coefficient may switch to a different value at the exponentially distributed time. The size of the drift jump is supposed to have a multinomial distribution. We have obtained the distribution function, the probability density function and the lower partial expectation for the considered process in closed forms. The results are applied to the calculation of the value at risk and the expected shortfall of the investment portfolio in the related multivariate stochastic model.

Suggested Citation

  • Roman V. Ivanov, 2022. "The Risk Measurement under the Variance-Gamma Process with Drift Switching," JRFM, MDPI, vol. 15(1), pages 1-27, January.
    • Handle: RePEc:gam:jjrfmx:v:15:y:2022:i:1:p:22-:d:720147
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    Citations

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    Cited by:

    1. Roman V. Ivanov, 2023. "On the Stochastic Volatility in the Generalized Black-Scholes-Merton Model," Risks, MDPI, vol. 11(6), pages 1-23, June.
    2. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.

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