Eine Einführung in die arbitragefreie Bewertung von Derivaten in stetiger Zeit am Beispiel europäischer Devisenoptionen

Abstract

An Introductory to Continuous-Scale Derivatives Evaluation in a Non-Arbitrage Environment on the Basis of the Example of European Foreign-Exchange Options

The legendary evaluation formulae of Black/Scholes (1973) and Garman/Kohlhagen (1983) are explained in great detail in a didactically attractive manner. To begin with, two fundamental discoveries concerning the option price theory are explained with the help of a simple binomial model: independence of optionrights evaluations from market participants’ risk-acceptance propensity and the resultant possibility of evaluating option rights in an imaginary risk-free environment. This is followed by a model reflecting the dynamism of prices - Brown’s geometric progression. This is the basis of the Garman/Kohlhagen differential equation, which provides the justification of the two aforementioned fundamental discoveries pertaining to the continuous-scale evaluations. With the help of evaluations in a risk-free environment, the Garman/Kohlhagen formula is subsequently developed, which includes the Black /Scholes formula describing a special case. Reading this introductory presupposes nothing more than “A-level knowledge of mathematics”.