scholarly journals Residue Sum Formula for Pricing Options under the Variance Gamma Model

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1143
Author(s):  
Pedro Febrer ◽  
João Guerra
Keyword(s):  
Complex Analysis ◽  
Asset Price ◽  
Option Price ◽  
Market Model ◽  
Call Option ◽  
Variance Gamma ◽  
Pricing Options ◽  
Variance Gamma Process ◽  
Multidimensional Complex Analysis ◽  
Multidimensional Complex

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.

scholarly journals SOME PRICING TOOLS FOR THE VARIANCE GAMMA MODEL

2020 ◽  
Vol 23 (04) ◽  
pp. 2050025 ◽  
Author(s):  
JEAN-PHILIPPE AGUILAR
Keyword(s):  
Complex Analysis ◽  
Convergent Series ◽  
Gamma Model ◽  
Variance Gamma ◽  
Model Driven ◽  
Variance Gamma Process ◽  
Multidimensional Complex Analysis ◽  
Multidimensional Complex ◽  
Variance Gamma Model ◽  
Inversion Techniques

We establish several closed pricing formulas for various path-independent payoffs, under an exponential Lévy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools from Mellin transform theory as well as from multidimensional complex analysis. Particular focus is made on the symmetric process, but extension to the asymmetric process is also provided. Speed of convergence and comparison with numerical methods (Fourier transform, quadrature approximations, Monte Carlo simulations) are also discussed; notable feature is the accelerated convergence of the series for short-term options, which constitutes an interesting improvement of numerical Fourier inversion techniques.

GIS-based risk monitoring of zoonotic cestodiasis in human

2016 ◽  
Vol 3 (4) ◽  
pp. 475-487
Author(s):  
Новосад ◽  
E. Novosad ◽  
Христиановский ◽  
Pavel Khristianovskiy
Keyword(s):  
Complex Analysis ◽  
Database Management System ◽  
Automatic Data ◽  
Risk Monitoring ◽  
Gis Tools ◽  
Wide Range ◽  
Epizootic Process ◽  
Multidimensional Complex Analysis ◽  
Multidimensional Complex

Objective of research: The target of the paper is to develop a model of GIS-based risk monitoring of zoonotic cestodiasis in human. Materials and methods: The use of geographic information systems (GIS) as an epizootiological and epidemiological method for the risk-based monitoring of human cestodiasis enables the development of a multi-level platform for solution of a wide range of tasks related to the control of this disease. The modern GIS tools use the methods of geoinformatics applying powerful software and hardware: open access geographic web servers, tools for multidimensional complex analysis, creating most accurate electronic and paper maps. Full-featured GIS contain a full set for processing geospatial data including acquisition of data, its integration and storage, automatic data processing, editing, creation and maintenance of topology, spatial analysis, access to the database management system (DBMS), visualization and creation of hard copies of any cartographic data. Results and discussion: The use of GIS enables to study more closely the regularities of epizootic process, geography of human cestodiasis and to improve the methodology both for short-term and long-term retrospective epizootiological analyses.

On Minimizing Risk in Incomplete Markets Option Pricing Models

1998 ◽  
Vol 01 (02) ◽  
pp. 227-233 ◽  
Author(s):  
Ola Hammarlid
Keyword(s):  
Incomplete Markets ◽  
Option Price ◽  
Market Model ◽  
Risk Minimization ◽  
Pricing Options ◽  
Fair Game ◽  
Local Risk ◽  
Game Condition ◽  
Stock Portfolio ◽  
Global And Local

I study the Bouchaud–Sornette, Schweizer and Schäl way of pricing options, presenting the methodology in accordance with Bouchaud–Sornette. The definitions of the wealth balance and risk from trading in options and stocks are presented. The problem of finding a risk minimizing strategy in an incomplete market model where a perfect hedge is not possible is analyzed. Using this strategy according to the approach of Bouchaud and Sornette the option is priced by a fair game condition. In this article I establish the equivalence between global and local risk minimization and prove an option price conjecture of Wolczyńska. I also investigate optimality for a stock portfolio with extra profit.

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

2021 ◽  
Vol 14 (2) ◽  
pp. 183-193
Author(s):  
Abdul Hoyyi ◽  
Abdurakhman Abdurakhman ◽  
Dedi Rosadi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Closed Form ◽  
Stock Price ◽  
Option Price ◽  
Secondary Data ◽  
Exponential Model ◽  
Variance Gamma ◽  
Variance Gamma Process ◽  
Normally Distributed

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.

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