Aims and Fit of Module

 To enhance students with a powerful mathematical machinery in order to apply  the risk-neutral pricing of various financial instruments via the fundamentals theorems of asset pricing

Learning outcomes

A. Apply the binomial option pricing model and arbitrage pricing in discrete, multi-period models.

B. Use probability spaces, filtrations, conditional probabilities, and expectations.

C. Explain the main results and basic applications of continuous-time stochastic processes: Brownian motion and martingales.

D. Apply Itô's calculus, in particular the stochastic Itô integral and Itô's formula.

E. Define and apply concepts related to continuous-time dynamic portfolio strategies using the Martingale Representation Theorem; apply the notions of arbitrage-free and complete markets; state and prove the First and Second Fundamental Theorems of Asset Pricing.

F. Use measure transformations to price European options via expectations under martingale measures, and apply the risk-neutral formula for option pricing.

G. Analyze the American put option mathematically.

H. Implement AI-assisted coding and perform dynamic hedging in a real-time trading environment.

Method of teaching and learning

 Lectures and homework exercises