A Consistent Model for the Pricing of Derivative Assets in a Discrete Time Framework

Abstract

Derivative assets are financial assets whose pay-outs depend in a non-stochastic way on prices and/or pay-outs of other assets, called primary assets. Thus, the randomness of derivative assets is completely driven by the randomness of primary assets. The most prominent examples of derivative assets are put and call options which only depend on the price process of the stock they are written on. Another obvious example which generally is not treated as a derivative asset is a portfolio of primary assets. A portfolio is an example of a derivative asset which depends on more than just one primary asset. Further examples of that kind are convertible securities, secured (collateralized) debt etc. Beside general asset pricing theory it is of its own interest to value derivative assets since it is hoped that they can be valued relative to the prices of primary assets thereby leading to quite simple results.