A mathematical model of pricing in a large system of cash bonds

F. Abikhalil, P. Dupont, J. Janssen and P. van Ossel

Applied Stochastic Models and Data Analysis, 1985, vol. 1, issue 1, 55-64

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.

Date: 1985
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https://doi.org/10.1002/asm.3150010107

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmda:v:1:y:1985:i:1:p:55-64

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