A mathematical model of pricing in a large system of cash bonds |
| |
Authors: | F Abikhalil P Dupont J Janssen P van Ossel |
| |
Abstract: | The purpose of this paper is to give a mathematical model to generalize the classical approach of compound interest and to overcome the time structure problem of the interest rates. We introduce a suitable stochastic process called the ‘gauge’ process such that its product with the value of any security is assumed to be a martingale in an appropriate probability space. The framework of this model gives a stochastic actualization formula for the pricing of general securities with options and includes Black and Schole's formula without using arbitrage arguments. Emphasis has been placed on numerical calculation. |
| |
Keywords: | Applied stochastic processes Martingales Ornstein— Uhlenbeck Cash bonds Option pricing Securities |
|