Interest Rate Derivatives

1. Front Matter

   Pages i-xviii

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2. Literature Review

   • Ingo Beyna

   Pages 1-1

3. The Cheyette Model Class

   • Ingo Beyna

   Pages 3-15

4. Analytical Pricing Formulas

   • Ingo Beyna

   Pages 17-26

5. Calibration

   • Ingo Beyna

   Pages 27-46

6. Monte Carlo Methods

   • Ingo Beyna

   Pages 47-71

7. Characteristic Function Method

   • Ingo Beyna

   Pages 73-100

8. PDE Valuation

   • Ingo Beyna

   Pages 101-130

9. Comparison of Valuation Techniques for Interest Rate Derivatives

   • Ingo Beyna

   Pages 131-136

10. Greeks

    • Ingo Beyna

    Pages 137-157

11. Conclusion

    • Ingo Beyna

    Pages 159-161

12. Back Matter

    Pages 163-209

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The class of interest rate models introduced by O. Cheyette in 1994 is a subclass of the general HJM framework with a time dependent volatility parameterization. This book addresses the above mentioned class of interest rate models and concentrates on the calibration, valuation and sensitivity analysis in multifactor models. It derives analytical pricing formulas for bonds and caplets and applies several numerical valuation techniques in the class of Cheyette model, i.e. Monte Carlo simulation, characteristic functions and PDE valuation based on sparse grids. Finally it focuses on the sensitivity analysis of Cheyette models and derives Model- and Market Greeks. To the best of our knowledge, this sensitivity analysis of interest rate derivatives in the class of Cheyette models is unique in the literature. Up to now the valuation of interest rate derivatives using PDEs has been restricted to 3 dimensions only, since the computational effort was too great. The author picks up the sparse grid technique, adjusts it slightly and can solve high-dimensional PDEs (four dimensions plus time) accurately in reasonable time. Many topics investigated in this book are new areas of research and make a significant contribution to the scientific community of financial engineers. They also represent a valuable development for practitioners.

• 91G30, 91G60
• Cheyette model
• interest rate derivatives
• multifactor HJM model
• numerical methods
• valuation
• quantitative finance

• of Finance & Management, Frankfurt School, Frankfurt, Germany

  Ingo Beyna

Beyna studied mathematics at the University of Freiburg i. Br., Germany, with a focus on applied mathematics. He started his PhD at the Frankfurt School in 2007 and worked as a consultant for Ernst & Young in the financial sector. He carried out parts of his research as a visiting fellow at the University of Technology, Sydney, Australia.

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