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Columbia University

Term-Structure and Credit Derivatives

Columbia University via Coursera

Overview

This course will focus on capturing the evolution of interest rates and providing deep insight into credit derivatives. In the first module we discuss the term structure lattice models and cash account, and then analyze fixed income derivatives, such as Options, Futures, Caplets and Floorlets, Swaps and Swaptions. In the second module, we will examine model calibration in the context of fixed income securities and extend it to other asset classes and instruments. Learners will operate model calibration using Excel and apply it to price a payer swaption in a Black-Derman-Toy (BDT) model. The third module introduces credit derivatives and subsequently focuses on modeling and pricing the Credit Default Swaps. In the fourth module, learners would be introduced to the concept of securitization, specifically asset backed securities(ABS). The discussion progresses to Mortgage Backed Securities(MBS) and the associated mortgage mathematics. The final module delves into introducing and pricing Collateralized Mortgage Obligations(CMOs).

Syllabus

  • Course Overview
  • Term Structure Models I
    • Welcome to week 2! This week, we will re-visit the fixed income instruments. So far we have been very comfortable with the notion of a fixed interest rate. In reality, however, interest rate is always evolving over time. Previously, we have seen that the evolution of stock prices can be modeled via multi-period binomial models or the Black Scholes model, but how do we capture the evolution of interest rate? Let us unfold the modeling of interest rate in this week. We will also see that all security derivatives have their equivalents in fixed income domains, such as options, forwards, futures and swaps. If you get stuck on the quizzes, you should post on the Discussions to ask for help. (And if you finish early, I hope you'll go there to help your fellow classmates as well.)
  • Term Structure Models II (and Introduction to Credit Derivatives)
    • Welcome to week 3! This week, we will start with an important practice in real-life financial engineering - model calibration. The mathematical models are no good if they do not capture the regularities in the financial markets. In order to ensure that our models are useful, we need to search for model parameters that describe the current market conditions. You might find it very helpful to review the optimization methods in the pre-requisite materials of Introduction of Financial Engineering and Risk Management.
  • Introduction to Credit Derivatives
    • Welcome to week 4! This week we will introduce credit derivatives, a very powerful family of derivative products that are partially responsible for the Financial Crisis in 2008. As always, if you get stuck on the quizzes, you should post on the Discussions to ask for help. (And if you finish early, I hope you'll go there to help your fellow classmates as well.)
  • Introduction to Mortgage Mathematics and Mortgage-Backed Securities
    • Welcome to week 5! This week, we will focus on a brand new set of financial products - mortgage-backed securities. Mortgage-backed securities are constructed from mortgages, which are common cash flows occurring in the housing market. Through a detailed case study of mortgage-backed securities, we will touch upon the important concept of securitization, i.e. how to package common cash flows into securitized products. We will explore a specific kind of financial product - Collateralized Mortgage Obligations (CMO). As always, if you get stuck on the quizzes, you should post on the Discussions to ask for help. (And if you finish early, I hope you'll go there to help your fellow classmates as well.)
  • Assignment - CMO
    • Welcome to week 6! This week, we will explore a specific kind of financial product - Collateralized Mortgage Obligations (CMO). We will also get some experience in pricing those securities. Finally, we will apply the knowledge we learned through the course by working on a quiz and a practical assignment. If you get stuck on the problems, you should post on the Discussions to ask for help. If you finish early, I hope you'll go there to help your fellow classmates as well.

Taught by

Martin Haugh and Garud Iyengar

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