On risk measuring in the variance-gamma model

Abstract

Abstract:In this paper, we discuss the problem of calculating the primary risk measures in the variancegamma 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.

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

“…For methods of numerical estimation of the CVaR, see the works by Chernozhukov and Umantsev (2001) and Chun et al (2012). For more recent studies, applications and investigations of the ES in various models, see in particular the works by Drapeau et al (2014), Ivanov (2018), Kalinchenko et al (2012) and Mafusalov and Uryasev (2016).…”

“…Next, the entropic risk measure (see for details and the importance of this measure, for example, the monograph by Föllmer and Schied (2004) and the works by Barrieu and El Karoui (2005), Föllmer and Schied (2010), Ivanov and Temnov (2017) and Ivanov (2018)) for the tail of distribution X is defined as…”

The Downside and Upside Beta Valuation in the Variance-Gamma Model

“…The basic monetary risk measures value at risk (see, for example, Berkowitz et al [6], Chen and Tang [8], Ivanov [20], Stoyanov et al [42]) and conditional value at risk (Kalinchenko et al [22], Mafusalov and Uryasev [29], Rockafellar and Uryasev [37]) serve to assess the downward risk of the investment portfolio.…”

“…As usually, the variance-gamma random variables are modeled as the normal mean-variance mixtures and it is supposed that the normal distributions are correlated. The paper develops the direction of research of Madan et al [26], Ano and Ivanov [3] and Ivanov [20], where closed form expressions in the variance-gamma framework are derived for various targets of mathematical finance.…”

Option pricing in time-changed Lévy models with compound Poisson jumps

“…In particular, it can be shown that this method cannot be applied to the pricing of digital options in the volatile variance-gamma model or in the normalinverse Gaussian one. The method of closed form solutions which had been introduced by Madan et al [33] was proceeded then in the papers by Ivanov and Ano [20], Ivanov [18] and Ivanov [19] for the variance-gamma distribution and by Ivanov [17] and Ivanov and Temnov [21] for the normal-inverse Gaussian one. This paper continues the elements of the research by Madan et al [33].…”