Cite JOURNAL ARTICLE
Eine Einführung in die arbitragefreie Bewertung von Derivaten in stetiger Zeit am Beispiel europäischer Devisenoptionen
Credit and Capital Markets – Kredit und Kapital, Vol. 27 (1994), Iss. 4 : pp. 591–627
Frank B. Lehrbass, Dortmund
Bauer, H., 1991: Wahrscheinlichkeitstheorie. Berlin: de Gruyter. - Black, F., Scholes, M., 1973: The Pricing of Options and Corporate Liabilities, J of Political Economy 81, 637 - 654.
Brauner, R., Geiß, F., 1990: Das Abitur-Wissen Mathematik. Frankfurt am Main: Fischer.
Brock, W. A., Malliaris, A. G., 1982: Stochastic Methods in Economics and Finance. New York: Elsevier.
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”.