## Vasilyeva T.A., Zelenyy D.D. Option calculator for asia options calculation by implicit difference scheme

Vasilyeva Tatyana Anatolyevna

Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Fundamental Informatics and Optimal Control Volgograd State University
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Prosp. Universitetsky, 100, 400062, Volgograd, Russian Federation

Zelenyy Denis Dmitrievich

Master Student, Department of Fundamental Informatics and Optimal Control
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Prosp. Universitetsky, 100, 400062, Volgograd, Russian Federation

Abstract. The popularity of options as secondary financial instruments is increasing and it stimulates the development of mathematical methods of their evaluation. Currently, the stock market has numerous types of options: European, American, barrier, Exotic, etc.
This article focuses on evaluating the Asian option. The mathematical model of considered problem is represented by the Black – Scholes model , which is a parabolic partial differential equation in relation to the price of Asian option. The use of implicit difference schemes for solving the problem can produce a stable numerical solution for different values of volatility, risk – free rate and the time of option exercise [1–3; 9]. For numerical solution algorithm was developed, implemented as a program Asia_option programming language C++. These calculations for the analysis of the results are generated in the form of tables and graphs in spread sheet format and Excelcharts.
Consider the example of the program of Asian put option. Define the following input parameters: r=0.05, σ=0.25, E=10, T=1. For simplicity, we choose a small time step
and define n=10. The graph (Figure 1) shows the surface of payments Asian put option for the following parameters T=1, r=0.05, S0=10, sigma=0.1. Asian option price at time t is at the intersection of the current value of the asset price S and the resulting surface V(S, t).
The program Asia_option is optional calculator, designed to calculate the value of Asian option based on the numerical solution of the Black-Scholes. In the program menu (Figure 2) are given by the input data for numerical calculations: T – expiry date of the option, r – the risk-free interest rate, σ – volatility, S0 – initial price of the asset. Value of each parameter is entered in the appropriate input box menu. Input field is selected by a computer mouse, which is entered in the necessary parameter key and press Tab. To begin the process necessary to press Start button and the results of calculations will be on the screen. Optional calculators are widely used in the analysis of the stock ticker, allow to predict the behavior of the value of options when changing various parameters such as volatility, interest rate, the price of the underlying assets, the period of the Strike.

Key words: Black-Sсholes model, options, Asia option, Exotic options, financial mathematics, derivatives, implicit difference schemes, option calculator.  3. Vasileva, Zelenyj.pdfURL: https://mp.jvolsu.com/index.php/en/component/attachments/download/253 3366 Downloads