Interest Rate Modeling
Learn the essential mathematics for term structure modeling and interest rate derivatives valuation in an accessible and intuitive fashion. Understand and apply the various approaches to constructing yield curves. Build interest rate models in discrete and continuous time.
CPE Credits: 21
This course is a component of the Advanced Fixed Income Professional Certificate.
Prerequisite knowledge:
- Intermediate to advanced MS Excel skills
- Some knowledge of differential and integral calculus
- Intermediate probability and statistics
- Basic linear algebra
- Familiarity with fixed income instruments, term structures, etc.
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Module 1: Review of Fixed Income Basics
- The no-arbitrage pricing principle
- Pricing vanilla fixed income instruments
- Risk measures: Duration and convexity
- Forwards and Futures
- Swaps
- Options
Module 2: Yield Curve Fundamentals
- Term structures: spot and forward rates
- Instantaneous interest rates
- Theories of the yield curve
- Economic implications of the shape of the yield curve
Module 3: A Taxonomy of Yield Curves
- Spot rate curves
- Swap curves
- Corporate curves
- Mortgage curves
Module 4: Yield Curve Fitting
- Fitting a curve to the bond market
- Nelson-Siegel and Nelson-Siegel-Svensson functions
- Polynomial and exponential splines
- Plotting bond yields against the fitted curve
- Yield spreads to the fitted curve
Module 4: Trading the Curve
- Interpretation and forecasting yield curve movements
- Fiscal and monetary policy
- Parallel yield curve shifts
- Non-parallel curve shifts (steepening/flattening/barbell)
- Econometric forecasting models
- Understanding and interpreting yield curves
- Yield curve strategies
- Total return analysis for yield curve shifts
Module 1: Taxonomy of Interest Rate Models
- One factor vs. multi-factor models
- Equilibrium models
- No-arbitrage models
- Spot rate models
- Term structure models
Module 2: Discrete Time Interest Rate Models
- Discrete time vs. continuous time
- Objective vs. risk-neutral probabilities
- No-arbitrage in discrete time
- Binomial models
- Recombining vs. non-recombining trees
- Normal vs. log-normal models
- Risk-neutral valuation on a binomial tree
- Risk-neutral expectation of future interest rates
- Trinomial trees
Module 1: Continuous Time Stochastic Processes
- The Wiener process as the limit of a random walk
- Brownian motion and Ito processes
- Functions of stochastic processes
- Ito's lemma
Module 2: Continuous Time Interest Rate Models
- No-arbitrage in continuous time
- The Black-Scholes-Merton partial differential equation
- Black's model for fixed income derivatives
- Vasicek bond pricing formula
- Cox, Ingersoll and Ross model
- Forward risk neutral pricing
- The Libor Market model
Module 3: Multi-Factor Interest Rate Models
- Ito's lemma with independent factors
- A two-factor Vasicek Model
- Black's model for fixed income derivatives
- Vasicek bond pricing formula
- Cox, Ingersoll and Ross model