 | Interest-Rate Models: Theory and Practical Applications
November 8-12, 2010 • YACINE AÏT-SAHALIA
Interest-rate models and fixed income instruments represent one of the most active areas of finance research and practice. Recent advances in this area are essential to the correct pricing and hedging of interest-rate-sensitive financial instruments and derivatives, to the accuracy of firm-wide risk management, as well as to gain an understanding of what went wrong during the financial crisis that started in 2007.
Objectives: This intensive course provides a full treatment of the state-of-the-art theory of interest-rate models and their practical applications. Participants will gain an understanding and enhance their knowledge of the fundamental mathematical tools and econometric techniques from the academic world, as well as the latest research used throughout the financial industry. Most of the models discussed and econometric techniques are implemented in spreadsheets which are reviewed at the end of each day in the form of hands-on exercises and given to the participants. The course is mathematically self-contained, but familiarity with calculus is expected. The instructor’s award-winning teaching approach is to emphasize the commonality between fixed income modelling and that relevant for other types of financial instruments and derivatives. As a result, participants will be able to apply many of the tools learned in the course beyond fixed income instruments and interest rate models to other types of derivatives. Among the course’s unique features is the integrated mix of the financial mathematics of interest rate modelling with the econometric aspects of such modelling: How to estimate or calibrate an interest rate model to the data? What feature(s) of a model is essential? Which model(s) fit best? Why?
Target audience: Traders, Central bankers, fixed-income analysts, quantitative researchers, financial engineers, asset managers, risk managers, derivatives salespeople, financial software developers, senior management of financial institutions.
Fees: The fee for this course is CHF 6’500 (incl. VAT). This covers tuition, extensive course material (including pre-course readings), lunches, and an official cocktail and dinner.
Accreditation: CFA 36 CE credits
Key topics: Interest rates; Term structure; Yield curve; Arbitrage; Risk management; Derivatives; Futures; Swaps; Financial crisis.
COURSE CONTENT
Monday
- Fixed income instruments review: Bonds, the term structure: Spot rates; forward rates; duration and convexity.
- Continuous-time calculus: Brownian motion; Itô’s Lemma; discrete-time approximation; Euler and Milstein schemes; trees.
- Arbitrage and risk-neutral pricing: Partial differential equations; risk-neutral density; Feynman-Kac formula; no-arbitrage prices.
Tuesday
- Applications of risk-neutral pricing to interest-rate derivatives: Forwards; bond options; caps; floors and collars; swaps; swaptions.
- Numerical methods for interest-rate models: Trees; risk-neutral and actual densities; partial differential equations; finite-differences, Crank-Nicholson algorithm; Feynman-Kac solution, Monte Carlo simulations; comparison of the methods.
Wednesday
- Classical interest-rate models: The Vasicek and Cox-Ingersoll-Ross models; other models; constructing trees.
- Multifactor interest-rate models: Affine and quadratic Gaussian models.
- Credit risk and default: Adding default to existing models.
Thursday
- Arbitrage free interest-rate models: Yield and volatility data; Ho-Lee model; extended Vasicek model; Black-Derman-Toy model; Heath-Jarrow-Morton model; non-recombining tree; forward-rate measures; changes of numeraire; the Libor market model.
- Calibrating interest-rate models to market data: The forward curve; bond price volatility; implied volatility of interest-rate caps.
Friday
- The econometrics of interest-rate modeling.
- Nonparametric density estimation for interest rates: Kernel estimator; bandwidth; practical implementation; nonparametric estimation of volatility; nonparametric pricing of interest-rate derivatives.
- Practical model building: How to model nonlinear mean reversion and volatility; testing the resulting model; how to decide whether a model fits the data; density-matching.
- Testing whether interest rates are Markovian: Non-Markovian dynamics in the HJM context.
- Testing for the presence of jumps in interest rates: Jumps dues to macroeconomic announcements; monetary policy.
- Maximum likelihood estimation for interest-rate models: Applications to multifactor term structure models and stochastic volatility.
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