Code

COMPG003

Year

MSc

Prerequisites

Knowledge of probability theory and stochastic processes, an introductory course in Financial Mathematics.

Term

2

Taught By

Andrea Macrina (50%), Carlo Marinelli (50%)

Aims/ Learning Outcomes

This is an introductory course in interest rate modelling and the pricing of fixed-income assets. The first part of the course focuses on the modelling of the term structure of bonds. During the second part of the course, the concept of credit risk and some standard credit risk models are introduced. 

Discount bonds, yield curves, stochastic discounting; classic short-rate models – e. g. Vasicek, Hull-White, and Cox-Ingersoll-Ross models; Heath-Jarrow-Morton framework; pricing kernel framework and positive interest rate models; market models; pricing formulae for caps, floors, swaptions; foreign exchange and inflation-linked pricing. Structural models of default: Black-Scholes-Merton model, first-passage models of default. Hazard function approach: hazard function and hazard rate, bond pricing with recovery at maturity or at the default-time. Pricing of simple defaultable claims.

3 hour lectures per week in term two

Two-hour written examination in term three. Student must achieve at least 50% to pass this course.

C. Bluhm, L. Overbeck, C. Wagner (2010) Introduction to credit risk modeling. Chapman & Hall/CRC Financial Mathematics Series.

D. Brigo, F. Mercurio (2006) Interest rate models – theory and practice: with smile, inflation and credit. Springer.

D. Filipovic (2009) Term-structure models: a graduate course. Springer.

M. Jeanblanc, M. Yor, M. Chesney (2009) Mathematical methods for financial markets. Springer.

S. E. Shreve (2008) Stochastic calculus for finance II: continuous-time models. Springer.