Elements of stochastic calculus:
Stochastic processes in continuous time. Brownian motion. Filtrations and
conditional expectations. Martingales. Ito's integral. Geometric
Brownian motion. Ito's formula. The Girsanov Theorem.
Financial Markets in continuous time:
The Black & Scholes model. Valutations of derivatives: the Black & Scholes PDE. Risk-neutral pricing. Delta-hedging and Delta-Gamma hedging. The Greeks. Multi-dimensional financial market models. The market price of risk. Complete and incomplete markets.
Credit risk models: Intensity-based models. Pricing of DZCB and CDS.
