Securities and derivatives are the foundation of modern financial markets. The fixed-income market, for example, is the dominant sector of the global financial market where various interest-rate linked securities are traded, such as zero-coupon and coupon bonds, interest rate swaps and swaptions. This unit will investigate short-term interest rate models, the Heath-Jarrow-Morton approach to instantaneous forward rates and recently developed models of forward London Interbank Offered Rates (LIBORs) and forward swap rates. You will learn about pricing and hedging of credit derivatives, another challenging and practically important problem and become familiar with stochastic models for credit events, dependent default times and credit ratings. You will learn how to value and hedge single-name and multi-name credit derivatives such as vulnerable options, corporate bonds, credit default swaps and collateralized debt obligations. You will also learn about the most recent developments in Financial Mathematics, such as robust pricing and nonlinear evaluations. By doing this unit, you will get a solid grasp of mathematical tools used in valuation and hedging of fixed income securities, develop a broad knowledge of advanced quantitative methods related to interest rates and credit risk and you will learn to use powerful mathematical tools to address important real-world quantitative problems in the finance industry.
lecture 3 hrs/week, tutorial 1 hr/week for 13 weeks
2 x homework assignments (20% each), final exam (60%)
1. M. Musiela and M. Rutkowski, "Martingale Methods in Financial Modelling." Springer, Berlin, 2nd Edition, 2005. 2. T. R. Bielecki, M. Jeanblanc and M. Rutkowski, "Credit Risk Modeling." Osaka University Press, Osaka, 2009.
Students are expected to have working knowledge of Stochastic Processes, Stochastic Calculus and mathematical methods used to price options and other financial derivatives, for example as in MATH4511 or equivalent