Synopsis for Fixed Income Markets

Stochastic calculus toolbox: multidimensional Ito processes, Ito's formula, martingale rep- resentation theorem and Girsanov's theorem. Extensions to processes with jumps. Change of numeraire technique.
Introduction to xed income markets. Interest rates, yield curves, basic products such as FRAs, bonds, swaps, caps, swaptions.
Modelling interest rates. Short rate modelling: modelling under P or Q, diusion models and term structure equation, ane models. Examples. Two factor models.
Forward rates modelling: HJM framework, bond prices and absence of arbitrage. Modelling market rates: forwards and futures, forward measures, Libor market models.

The main references for the course are;

1. D. Filipovic, Term-Structure Models, Springer (2009)
2. S. Shreve Stochastic Calculus for finance II (Continuous-Time Models)
   Additional insights might be found in
3. Protter, Stochastic integration and differential equations
4. Bjork, Arbitrage theory in continuous time - "available online from Oxford Scholarship Online: http://www.oxfordscholarship.com/oso/public/content/economicsfinance/9780199271269/toc.html
5. Brigo and Mercurio, Interest rate models - theory and practice