Stochastic modelling and derivatives

This course provides an overview of stochastic modeling in financial markets. Its aim is to present the foundations of arbitrage theory for derivative pricing and to introduce key concepts in financial risk management. The course begins with a review of basic financial products, the principles of option pricing, arbitrage, and discrete-time models such as the Cox-Ross-Rubinstein framework. It then develops continuous-time modeling through the Black-Scholes model, covering its properties and associated hedging techniques. Advanced topics include the pricing of exotic options, alternative volatility models such as local and stochastic volatility (e.g., Heston, SABR), and Fourier-based pricing methods. The course concludes with a discussion of market data and statistical analysis.