Financial Mathematics

In this course a special emphasis will be put on the mathematical derivation of pricing and hedging formulas for financial products, in order to apply and extend the knowledge of the students in probability and partial differentiation. The course is divided into a presentation of the main concepts of arbitrage and market completeness in discrete time, which requires only an elementary mathematical background, and a more technical second part on continuous-time models, which focuses on the rules of stochastic calculus for the modeling of asset prices. The topics covered will include the pricing and hedging of financial options, with a derivation of the Black-Scholes formula by both probabilistic and analytic arguments. We will also make the connection with market data via the use of implied volatility and basic numerical methods for pricing.