Black-Scholes model

The Black-Scholes model finds an appropriate (fair) price for an option or warrant. The fair price is calculated on the basis of the term, the strike price, the volatility and the price of the underlying, the interest rate for safe investments, the subscription ratio and, if applicable, foreign exchange rates.

This valuation model has now established itself internationally and is also used on Eurex.

As the formula for the Black-Scholes model is relatively complex, a computer-based evaluation is the obvious choice. Your Infront Portfolio Manager calculates the fair price using the Black-Scholes model and, based on this, prepares most of the quantitative analysis evaluations.

The Black-Scholes model was originally developed for calls and puts on shares. As options on other types of underlyings were also traded over time, model adjustments were necessary for the special features of the respective underlyings.

With options on foreign exchange and bonds, for example, you are dealing with a constant return on the underlying asset - in contrast to the situation with shares. The Garman/Kohlhagen model has therefore been applied here. Bühler has adapted the standard Black-Scholes model for options on interest rate futures.

All model variants are implemented in the Infront Portfolio Manager. The model on which the quantitative analysis is based is decided automatically on the basis of the option or warrant master data.

A more detailed introduction to the field of option valuation can be found in M. Steiner, C. Bruns, S. Stöckl: Securities Management, Schäffer/Poeschel, 11th edition, 2017.