Yield Curves

Construction, Modelling and Applications

Agenda Program
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Prague, NH Hotel Prague
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Fundamentals of Yield Curve Construction
Bootstrapping and Cubic Splining
Blending, Interpolating and Smoothing Techniques
Credit Spreads and Forward Credit Spreads
Cash Flow Mapping, Delta Vectors and Key Rate Duration
Principal Components Analysis
Using Yield Curves in Trading and Risk Management
The purpose of this seminar is to give you a good understanding of techniques for constructing yield curves and for the applications of yield curves in trading and risk management.

We start with an in-depth explanation of fundamental concepts such as yields, discount factors, spot rates and forward rates. We present different types of yield curves such as the zero coupon and par curves, and we give an overview of their uses in securities pricing, investment analysis and risk management.

We then explain how the swap curve can be "Bootstrapped" using deposits, FRAs, convexity adjusted interest rate futures and par swaps as building blocks. We also demonstrate how the swap curve is used for the pricing of standard and non-generic swaps.

Next, we explain how bond yield curves can be constructed from available market data. We start with the construction of the zero coupon curve using the "Cubic Splining" technique on bond data. We explain how the resulting discount factors can be used to identify arbitrage opportunities in the bond market.

We also explain how swap and bond curves can be fitted using the "Nelson-Siegel" formula.

Finally, we explain how yield curves can be used in day-to-day trading and risk management. We show how security and portfolio cash flows can be mapped to yield curve grid points and we explain how "Delta Vectors" and key ratios such as "Key Rate Duration" are derived and used to control interest rate risk. We also explain how "Principal Components" analysis can be used to decompose variations in the yield curve into independent factors and how a "factor-immunized" portfolio can be constructed.

Program of the seminar: Yield Curves

The seminar timetable follows Central European Time (CET).

09.00 - 09.15 Welcome and Introduction

09.15 - 12.00 Fundamentals of Yield Curve Construction

  • Yield Curves and their Applications in Finance
  • Building Blocks in Yield Curve Construction
    • Price and yield analysis
    • Spot rates and discount factors
    • Continuously compounded yields
    • Forward rates
  • Types of Yield Curves
    • Simple yield curve
    • The par curve
    • The duration yield curve
    • Libor curves
  • Current and Historical Yield curves
  • Factors Explaining the Shape of the Yield Curve
    • Liquidity theory
    • Expectations theory
    • Market segmentation theory
  • Exercises

12.00 - 13.00 Lunch

13.00 - 16.30 Constructing and Using Libor Curves

  • Building Blocks in Libor Curve Construction
    • Deposits
    • FRAs and interest rate futures
    • Par swaps
  • Convexity Adjustment of Futures Prices
  • Bootstrapping
    • Constructing the short end
    • Extending the curve
  • Interpolation and Smoothing Techniques
    • Linear and non-linear techniques
    • The Nelson-Siegel Estimation Technique
  • Pricing FRAs, Swaps and other Libor Instruments
    • Pricing generic par and off-market swaps
    • Pricing forward starting, amortizing, arrears reset and other non-generic swaps
  • Examples and Exercises

09.00 - 09.15 Brief recap

09.15 - 12.00 Constructing Yield Curves with Bonds

  • Components of Bond Yields
  • Problems Using the Bootstrapping Technique with Bonds
  • Empirical Estimation of the Yield Curve
    • Regression techniques
    • Selecting the bond sample
    • Taking liquidity and tax effects into account
    • Functional form of the discount function
  • Using Cubic Splines
    • Why use splines?
    • Choosing the spline points
    • 1st and 2nd order constraints
    • Joining the splines
  • Constructing Credit Curves
    • An option-theoretical approach for determining credit spreads
    • Bootstrapping the credit curve
    • Calculating forward credit spreads
  • Exercises

12.00 - 13.00 Lunch

13.00 - 16.30 Using Yield Curves in Trading and Risk Management

  • Identifying Arbitrage Opportunities
    • Calculation option adjusted spread
    • Cheap-rich Analysis
    • Bond switching
  • Risk Management
    • Calculating delta vectors
    • Calculating key rate durations
    • Decomposing yield curve variations
    • Principal components analysis
    • Calculating factor sensitivities
    • Factor-immunization
    • Selective hedging
  • Exercises

Summary, Evaluation and Termination of the Seminar

Training catalogue in PDF
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