Through this project, you should now have a deeper understanding of how concepts from physics, particularly stochastic pro​

​cesses and mathematical modelling, are applied in finance. Specifically, you should have learned: 

1. The Role of Stochastic Processes in Financial Models 

• How random processes like Brownian motion form the foundation of financial modelling. 

• The significance of geometric Brownian motion in describing asset prices. 

2. The Black-Scholes Model and Its Assumptions 

• The mathematical basis of the Black-Scholes model and its use in pricing options. 

• The key assumptions behind the model, including constant volatility and risk-free interest rates. 

3. Limitations and Real-World Challenges 

• Why financial markets do not always behave as expected due to external shocks, human behaviour, and liquidity constraints. 

• The impact of extreme events such as market crashes, which challenge the assumptions of smooth price changes. 

4. Adapting Physics-Based Models for Finance 

• While physics provides a strong foundation for financial models, direct application often requires modifications to account for economic and behavioural factors. 

• How models like jump-diffusion and stochastic volatility frameworks adjust traditional physics-based assumptions to better match real-world financial data. 

5. Lessons from LTCM: The Risks of Over-Reliance on Models 

• How the collapse of Long-Term Capital Management (LTCM) demonstrated the dangers of assuming financial markets follow predictable, physics-inspired equations. 

• The importance of balancing quantitative models with risk management and real-world awareness. 

By now, you should appreciate both the power and the limitations of applying physics-based models to finance. While these models provide useful tools for understanding market behaviour, they must be adapted and applied with caution, recognizing the unpredictable and human-driven nature of financial systems.