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Unit of study_

MATH4513: Topics in Financial Mathematics

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.

Code MATH4513
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites:
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None
Corequisites:
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None
Prohibitions:
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None
Assumed knowledge:
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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

At the completion of this unit, you should be able to:

  • LO1. Demonstrate familiarity with fundamental concepts in the area of financial markets with application to existing securities related to interest rates, such as: bonds, bond options and interest rate swaps and swaptions.​
  • LO2. Develop stochastic models and solve qualitative and quantitative problems associated with the valuation and hedging of fixed income securities within the framework of short-term rate models.​
  • LO3. Understand, explain and apply the principles of modelling of forward rates through different competing methods and analyse the relationships between alternative approaches​.
  • LO4. Apply mathematical expertise to solve practical problems using various approaches and analyse the advantages and shortcomings of solutions obtained through different methods.​
  • LO5. Examine the concept of credit risk and its impact on pricing problems for complex financial derivatives such as: corporate bonds, credit default swaps and collateralized debt obligations.​
  • LO6. Analyse the issue of dependence between defaults of several credit-risky names and apply various probabilistic techniques for modelling of dependent defaults. ​
  • LO7. Identify, formulate and solve original practical problems that can be addressed using mathematical techniques learnt in this unit, interpret these solutions and evaluate their implementations.​
  • LO8. Demonstrate capability for independent learning using sources such as journal articles and working papers and use this information to evaluate recently developed approaches and mathematical tools.​

Unit outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.