Arbitrage Theorem and its Applications

Authors

  • Tamás Nagy University of Miskolc

Keywords:

Financial rate, Arbitrage theorem

Abstract

In my article I describe the concept of financial rate of return and the value of return in a very simple model first. Then as
generalisation of the model we take an experiment, which has n possible outcomes. We have the same m kind betting possibilities
for each outcome. The financial rate of return is known for each outcome and betting possibility. We define the concept of
arbitrage (the possibility of sure winning), and we are looking for the answer how to characterise the arbitrage exemption. What
is the guarantee, that any betting terms cannot be given for which the winning is sure for each outcome? For this question the
answer is given in the arbitrage theorem, which is one of the alternatives of the well-known Farkas theory. In the second part of
the article I demonstrate some applications of the theorem. I apply it for a classical betting problem first, then for an option
pricing in more details. The applications for the one-period binomial and trinomial, and the more-period binomial option pricing
will also be made known.

References

Bodie, Kane, Marcus: /1996/ Befektetések I., II. Budapest

Brealey, Myers: /1993/ Modern vállalati pénzügyek. Budapest

Farkas Gy.: /1902/ Über die Theorie der einfachen Ungleichungen. Journal für die Reine und Angewandte Mathematik 124, 1-27.

Farkas Gy.: /1918/ A lineáris egyenlôtlenségek következményei, Matematikai és Természettudományi Értesítô 36, 397-408.

Hull, J.: /1999/ Opciók, határidôs ügyletek és egyéb származtatott termékek. Budapest

Korn R.: /1998/ Optimal Portfolios. World Scientific

Luenberger D.: /1998/ Investments Science. Oxford University Press

Ross S.: /1999/ An Introduction to Mathematical Finance. Cambridge University Press

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Published

2002-02-23

How to Cite

Nagy, T. (2002). Arbitrage Theorem and its Applications. Theory, Methodology, Practice – Review of Business and Management, 1(01), 27–32. Retrieved from https://ojs.uni-miskolc.hu/index.php/tmp/article/view/1294

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Articles