The risk measurement under the variance-gamma process with drift switching - Roman V. Ivanov (Journal of Risk and Financial Management, 2022)
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.
Keywords: 330; variance-gamma process; drift switching; exponential distribution; hypergeometric function; lower partial expectation; value at risk; expected shortfall