A review of two financial market models: the Black--Scholes--Merton and the Continuous-time Markov chain models

• Main Authors: Ayana, Haimanot, Al-Swej, Sarah
• Format: Others
• Language: English
• Published: Mälardalens högskola, Akademin för utbildning, kultur och kommunikation 2021
• Subjects: Black-Scholes-Merton model; Continuous-time Markov chain model and financial market components; Natural Sciences; Naturvetenskap
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-55417

The objective of this thesis is to review the two popular mathematical models of the financialderivatives market. The models are the classical Black–Scholes–Merton and the Continuoustime Markov chain (CTMC) model. We study the CTMC model which is illustrated by themathematician Ragnar Norberg. The thesis demonstrates how the fundamental results ofFinancial Engineering work in both models.The construction of the main financial market components and the approach used for pricingthe contingent claims were considered in order to review the two models. In addition, the stepsused in solving the first–order partial differential equations in both models are explained.The main similarity between the models are that the financial market components are thesame. Their contingent claim is similar and the driving processes for both models utilizeMarkov property.One of the differences observed is that the driving process in the BSM model is the Brownianmotion and Markov chain in the CTMC model.We believe that the thesis can motivate other students and researchers to do a deeper andadvanced comparative study between the two models.