2023, Vol. 8, Issue 4, Part A

One of the diffusion processes that is used to model the velocity of a particle that undergoes Brownian motion is the Orstein - Uhlenbeck, which can also be used to model the volatility of an underlying process. Black - Scholes model gives a very good approximation to the analysis of market derivatives despite its various assumptions. One benefit of the Orstein - Uhlenbeck model is that it leads to tractable solutions to a number of financial challenges. This study, therefore, formulates the Black - Scholes equation using Orstein - Uhlenbeck model, this will help solve some of the financial challenges faced in the Black - Scholes equation like constant volatility. This study uses the analysis of the Black - Scholes equation to derive a new model of the Black - Scholes equation using Orstein - Uhlenbeck model.