How to Identify an Arbitrage of Type B on Capital Markets

Abstract

We propose here a 1-period matrix model of a fraction of the Polish financial market (for our purposes it will suffice to focus on a fraction of the market) built up from the point of view of the Polish biggest listed company KGHM. Using this model we construct an arbitrage portfolio consisting of 5 different assets, namely shares of KGHM, Treasury bills and 3 kinds of stock options. We recall the concept of arbitrage of type A and type B (called also an arbitrage I and arbitrage II, resp.) and illustrate it with examples. To prove that an arbitrage is possible to conduct, we separately distinguish scenarios when options prices are determined by the Black-Scholes formula, and when they deviate from their theoretical values. We prove that in all those cases an arbitrage of type B can be conducted. Since our approach does not rely on the specifics of Poland as a country, it can be equally well implemented in any other country which offers Treasury bills, as well as call and put options on shares of selected companies (KGHM in the studied case). The purpose of this study is to encourage practitioners to conduct an arbitrage in their own country, especially in a case when call and put options are offered on a local OTC market.