Generalizing the Black and Scholes Equation Assuming Differentiable Noise

Kjell Hausken, John F. Moxnes and Fernando Simoes

Journal of Applied Mathematics, 2024, vol. 2024, 1-18

Abstract: This article develops probability equations for an asset value through time, assuming continuous correlated differentiable Gaussian distributed noise. Ito’s (1944) stochastic integral and a generalized Novikov’s (1919) theorem are used. As an example, the mathematical model is used to generalize the Black and Scholes’ (1973) equation for pricing financial instruments. The article connects the Kolmogorov (1931) probability equation to arbitrage and to how financial instruments are priced, where more generally, the mathematical model based on differentiable noise may improve or be an alternative for forecasts. The article contrasts with much of the literature which assumes continuous nondifferentiable uncorrelated Gaussian distributed white noise.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jam/2024/8906248.pdf (application/pdf)
http://downloads.hindawi.com/journals/jam/2024/8906248.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:8906248

DOI: 10.1155/2024/8906248

Access Statistics for this article

More articles in Journal of Applied Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().