The Trinomial Tree and the PLC Theory in Footballers’ Valuation

Abstract

Nowadays, football is not just only an amateur sport, but also a big and a very interesting branch of industry for investors and gamblers. Football clubs start to act like an ordinary company on the market. One of the most important assets in a club’s balance are footballers’ performance rights. Every year thousands of players are the subject of football club transfers (in 2013 there were over 12.000 of such transfers with a total value of over USD 37 billion). It means that the monitoring of a footballer’s value could protect a club before the risk of a sudden disadvantageous change.

This article indicates the possibilities of using quantitative methods in players’ performance rights value monitoring. Authors have raised the hypothesis that joins methods of the trinomial tree and the product life cycle that could give the managers of clubs more powerful tools in managing a football club company. The trinomial tree is usually used to value the option price giving three paths of price movement. In this approach, the method was used to determine the future hypothetical value of footballers’ performance rights. Using the product life cycle we could observe and analyse the moment in the life cycle of a football player. In this part of the research, non-linear models were used to approximate the best-fitting function of the market value of a player. Such information indicates the direction of movement on the trinomial tree.

In this article, we use the historical data of the market values of chosen football players from the web site http://transfermarkt.de. To make a proper analysis, we chose three kinds of players: in the phase of growth, in the phase of stabilization and the phase of dropping down in value. Such an assumption causes the necessity of choosing players with adequate features, for example: age, skills and the team played for. Therefore, the length of the time series depends on the years and the performances of the footballer. The opportunities and threats of such an attempt are shown in this article.