Home  Journals  Financial Analytics: Science and Experience  24(306) - 2016 June

The application of fuzzy numbers to pricing of shares as part of the agent-based model of the financial market

Vol. 9, Iss. 24, JUNE 2016

Article PDF Version

Received: 20 May 2016

Received in revised form: 2 June 2016

Accepted: 15 June 2016

Available online: 29 June 2016

Subject Heading: MATHEMATICAL ANALYSIS AND MODELING IN ECONOMICS

JEL Classification: C14, G13

Pages: 30-41

Importance The research investigates models of financial markets and proposes to modify the agent-based model, where uncertainty, due to investors' individual attitude to the risk, is modeled with fuzzy numbers.
Objectives The research pursues making an agent-based model of the financial market, which describes the interaction of investors using various approaches to deciding on the purchase of shares and methods of the fuzzy numbers theory. I also model the share price when each investor has its unique attitude to the risk and examine how the balance of investors' types and possibilities of portfolio hedging influence the dynamics of the share price.
Methods The research reviews the agent-based model of the financial market, where trends in the share price depend on activities of many investors. Each investor forms its own portfolio adhering to the Black–Litterman model and can resort to hedging of the portfolio for risk management purposes. Fuzzy numbers are used to model uncertainty of such indicators as the share price, risk-free rate and investor's susceptibility to the risk.
Results I built a financial market model, which allows forecasting the share trends and evaluate the level of forecast uncertainty. I estimated the cost of portfolio hedging for fuzzy input data and analyzed how trends in the fuzzy price of the share depended on the trade-off between investors and a possibility to hedge the portfolio.
Conclusions and Relevance When the financial market demonstrates the prevailing number of investors that take up decisions on the basis of previous trends, it can result in a critical drop in the share price, even if the share yield insignificantly decreased. Portfolio hedging pegs the share price at the certain level during a slump in the share price. The uncertainty of the projected share price decreases when slumping prices are forecasted.

Keywords: risk management, fuzzy numbers, hedging, portfolio, model

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