Analyzing Stochastic Processes in Stock Market Modeling for Investment Banking Applications

1. Introduction 2. Basics of Stochastic Processes 2.1 Definition and Characteristics 2.2 Types of Stochastic Processes 2.3 Applications in Finance 3. Stock Market Models 3.1 Historical Development 3.2 Fundamental Models 3.3 Technical Analysis Models 4. Key Stochastic Models 4.1 Brownian Motion 4.2 Geometric Brownian Motion 4.3 Markov Chains 4.4 Poisson Processes 5. Risk Assessment Techniques 5.1 Value at Risk (VaR) 5.2 Monte Carlo Simulations 5.3 Stress Testing 6. Model Calibration Methods 6.1 Parameter Estimation 6.2 Backtesting Strategies 6.3 Model Validation 7. Application in Investment Banking 7.1 Portfolio Optimization 7.2 Derivatives Pricing 7.3 Risk Management Strategies 8. Challenges and Limitations 8.1 Model Assumptions 8.2 Computational Complexity 8.3 Market Anomalies 9. Conclusion and Future Directions