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

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.

VARIANCE GAMMA PROCESS WITH MONTE CARLO SIMULATION AND CLOSED FORM APPROACH FOR EUROPEAN CALL OPTION PRICE DETERMINATION

The Option is widely applied in the financial sector. The Black-Scholes-Merton model is often used in calculating option prices on a stock price movement. The model uses geometric Brownian motion which assumes that the data is normally distributed. However, in reality, stock price movements can cause sharp spikes in data, resulting in nonnormal data distribution. So we need a stock price model that is not normally distributed. One of the fastest growing stock price models today is the process exponential model. The process has the ability to model data that has excess kurtosis and a longer tail (heavy tail) compared to the normal distribution. One of the members of the process is the Variance Gamma (VG) process. The VG process has three parameters which each of them, to control volatility, kurtosis and skewness. In this research, the secondary data samples of options and stocks of two companies were used, namely zoom video communications, Inc. (ZM) and Nokia Corporation (NOK). The price of call options is determined by using closed form equations and Monte Carlo simulation. The Simulation was carried out for various values until convergent result was obtained.

Residue Sum Formula for Pricing Options under the Variance Gamma Model

We present and prove a triple sum series formula for the European call option price in a market model where the underlying asset price is driven by a Variance Gamma process. In order to obtain this formula, we present some concepts and properties of multidimensional complex analysis, with particular emphasis on the multidimensional Jordan Lemma and the application of residue calculus to a Mellin–Barnes integral representation in C3, for the call option price. Moreover, we derive triple sum series formulas for some of the Greeks associated to the call option and we discuss the numerical accuracy and convergence of the main pricing formula.

Prognostic and Classification of Dynamic Degradation in a Mechanical System Using Variance Gamma Process

Recently, maintaining a complex mechanical system at the appropriate times is considered a significant task for reliability engineers and researchers. Moreover, the development of advanced mechanical systems and the dynamics of the operating environments raises the complexity of a system’s degradation behaviour. In this aspect, an efficient maintenance policy is of great importance, and a better modelling of the operating system’s degradation is essential. In this study, the non-monotonic degradation of a centrifugal pump system operating in the dynamic environment is considered and modelled using variance gamma stochastic process. The covariates are introduced to present the dynamic environmental effects and are modelled using a finite state Markov chain. The degradation of the system in the presence of covariates is modelled and prognostic results are analysed. Two machine learning algorithms k-nearest-neighbour (KNN) and neural network (NN) are applied to identify the various characteristics of degradation and the environmental conditions. A predefined degradation threshold is assigned and used to propose a prognostic result for each classification state. It was observed that this methodology shows promising prognostic results.

Avatars-Based Decision Support System Using Blockchain and Knowledge Sharing for Processes Simulation

This article is an enhancement of the chapter “About Digital Avatars for Control in Virtual Industries” in the book Big Data and Knowledge Sharing in Virtual Organizations. The article discusses the capabilities of the R language for modeling Levy processes that currently most closely correspond to the nature of the organizational learning movements in sliding mode. The efficient algorithm of the CGMY process simulation as a difference of the tempered stable independent Levy is processed and programmed at R language. The efficient algorithm of variance gamma process simulation using variance gamma random variables is processed and programmed at R language. Overview of CGMY process simulation in practice is use for human capital management in the context of the implementation of digital intelligent decision support systems and knowledge management and for digital intelligent design of avatar-based control with application to human capital management.

VALUATION OF EUROPEAN PUT OPTION BY USING THE QUADRATURE METHOD UNDER THE VARIANCE GAMMA PROCESS

Dynamic asset pricing model uses the Geometric Brownian Motion process. The Black-Scholes model known as standard model to price European option based on the assumption that underlying asset prices dynamic follows that log returns of asset is normally distributed. In this paper, we introduce a new stochastic process called levy process for pricing options. In this paper, we use the quadrature method to solve a numerical example for pricing options in the Indian context. The illustrations used in this paper for pricing the European style option. We also try to develop the pricing formula for European put option by using put-call parity and check its relevancy on actual market data and observe some underlying phenomenon.

Sharing and Avatar-Based Innovation Tools on Digital Economy Perspectives Using Levy Processes Simulation

This article is the Enhancement of the Mkrttchian and Vertakova article “Digital Sharing Economy” published in the International Journal of Innovation in Digital Economy (IJIDE, Volume 10, issue 2) and the chapter “Avatar-Based Innovation Tools for Managerial Perspectives on Digital Sharing Economy” in the book “Avatar-Based Models, Tools, and Innovation in the Digital Economy,” focused on an entirely new area relevant to the scope of IJIDE. The article discusses the capabilities of the R language for modeling Levy processes - processes that currently closely correspond to the nature of the evolution of stock price movements. The efficient algorithm of the CGMY process simulation as a difference of the tempered stable independent Levy is processed and programmed at R language. The efficient algorithm of variance gamma process simulation using variance gamma random variables is processed and programmed at R language, as Modelling in the Digital Globalization Era.