Lecture 1 (2 hours): Introduction to Mathematical Modelling and Mathematical Finance

• Examples of Modelling: ODE, PDE, Interest Rate Modelling Process
• Modelling Involved Stochastic/Random Behaviour: Wiener and Gaussian Processes
• Stock Prices Modelling (Geometric Brownian Motion) and Forwards Simulation
• Roots and History of Math Finance
• Classics: Cox-Ross-Rubinstein (CRR) (discrete-time case) and Black-Scholes (continuous-time case) Models and Formulas, Call-Put Parity
• New Directions and Some Prospective in Math Finance

Lecture 2 (2 hours): Stochastic Modelling of Big Data in Financial and Energy Markets

• Big Data in Finance: High-Frequency and Algorithmic Trading (HFT) Data Limit Order Books (LOB)
• Stochastic Modelling of Big Data in Finance
• Forwards, Futures, Options on Forwards and on Futures Black-76 Formula (Positive Prices)
• Alternative to Black-76 Formulas (Negative Prices)
• Some Results for Alternative Models
• A Vision to Transition to 100

PS: 10 Multiple choice questions will be provided to test the students' training activities.

Note:

Session 1: (9:00-10:20)

Coffee break: (10:20-10:40)

Session 2: (10:40-12:00)

Lunch break: (12:00-13:30)

Session 3: (13:30-14:50)