A Credit-Risk Valuation under the Variance-Gamma Asset Return

Abstract

This paper considers risks of the investment portfolio, which consist of distributed mortgages and sold European call options. It is assumed that the stream of the credit payments could fall by a jump. The time of the jump is modeled by the exponential distribution. We suggest that the returns on stock are variance-gamma distributed. The value at risk, the expected shortfall and the entropic risk measure for this portfolio are calculated in closed forms. The obtained formulas exploit the values of generalized hypergeometric functions.

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

“…Section 5 applies the results to the computation of the value at risk and the expected shortfall monetary risk measures. The paper proceeds the direction of research of the works by Madan et al (1998); Ano and Ivanov (2016); Ivanov (2018); Ivanov and Temnov (2016) where analytical results were obtained in the variance-gamma model and its generalizations.…”

“…ς (u) − α = 0 with a one of the root-finding algorithms, seeBrent (1973);Press et al (2007); Stoer and Bulirsch (2002) for details. The computation of the distribution function of losses in analytical or semi-analytical forms in various models is given inArmenti et al (2018); Drapeu et al (2014);Ivanov (2018) Chun et al (2012)Mafusalov and Uryasev (2016) estimate the value at risk and the expected shortfall using the Monte Carlo simulations.…”

The Semi-Hyperbolic Distribution and Its Applications

“…The computations of the measures in semi-analytical forms by the Fourier transform technique are given in Armenti et al [60] and Drapeu et al [61]. Analytical formulas for some specific models are provided by Ivanov [62,63] and Rockafellar and Uryasev [64]. Monte Carlo simulations of the VAR and ES were made by Chun et al [65] and Mafusalov and Uryasev [66].…”

On the Stochastic Volatility in the Generalized Black-Scholes-Merton Model

“…Finlay and Seneta (2008) develop different techniques for parameter estimation in the skew Student's t-model and discuss the modeling of the S&P500 index and the oil prices. The variance-gamma process (the variance-gamma distribution is the normal-inverse mixture with the gamma mixing density, and hence the variance-gamma process has the stochastic drift modeled by the gamma process) is considered in Madan et al (1998), Seneta (2004), Daal and Madan (2005), Ivanov (2018), Ivanov (2022), Linders andStassen (2016), andMozumder et al (2015), among others. Madan et al (1998) summarize the basic properties of the variance-gamma distribution and suggest the method of receiving analytical results in the variance-gamma model.…”