Skip to main content
Article thumbnail
Location of Repository

Uncertain interest rate modelling

By D. Epstein


In this thesis, we introduce a non-probabilistic model for the short-term interest rate. The key concepts involved in this new approach are the non-diffusive nature of the short rate process and the uncertainty in the model parameters. The model assumes the worst possible outcome for the short rate path when pricing a fixed-income product (from the point of view of the holder) and differs in many important ways from the traditional approaches of fully deterministic or stochastic rates. In this new model, delta hedging and unique pricing play no role, nor does any market price of risk term appear. We present the model and explore the analytical and numerical solutions of the associated partial differential equation. We show how to optimally hedge the interest rate risk of a fixed-income portfolio and price and hedge common and exotic fixed-income products. Finally, we consider extensions to the model and present conclusions and areas for further research

Topics: Partial differential equations, Game theory, mathematical finance, economics, social and behavioral sciences, Numerical analysis
Year: 1999
OAI identifier:

Suggested articles


  1. (1996). A comparison of diffusion models of the term structure.
  2. (1999). A multifactor model for the term structure and inflation for long-term risk management. Working paper,
  3. (1998). A new model for interest rates.
  4. (1999). A nonlinear non-probabilistic spot interest rate model.
  5. (1998). A note on the pricing of index amortising rate swaps in a worst-case scenario. OCIAM Working Paper,
  6. (1990). A one-factor model of interest rates and its application to treasury bond options. Financial Analysts Journal, doi
  7. (1997). A sterling leasing portfolio,
  8. (1985). A theory of the term structure of interest rates.
  9. (1992). A two-factor interest rate model and contingent claim valuation.
  10. (1977). An equilibrium characterization of the term structure.
  11. (1982). An equilibrium model of bond pricing and a test of market efficiency. doi
  12. (1996). An Introduction to the Mathematics of Financial Derivatives.
  13. (1980). Analyzing convertible bonds. doi
  14. (1999). Applied Partial Differential Equations.
  15. (1996). Bond Markets, Analysis and Strategies.
  16. (1992). Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation.
  17. (1997). Breaking barriers. Risk magazine,
  18. (1997). Combinatorial implications of nonlinear uncertain volatility models: the case of barrier options. Courant Institute,
  19. (1997). Crash courses. Risk magazine,
  20. (1998). Derivatives: The Theory and Practice of Financial Engineering.
  21. (1997). Dynamic Hedging.
  22. (1991). Eurodollar Futures and Options.
  23. (1995). Expect the worst. Risk magazine,
  24. (1997). Financial Modeling.
  25. (1994). Fitting yield curves and forward rate curves with maximum smoothness.
  26. (1996). Fixed income security valuation in a worst case scenario. DPhil Transfer Thesis,
  27. (1998). Implementing derivatives models.
  28. (1998). Instructors Manual for Derivatives: The Theory and Practice of Financial Engineering.
  29. (1996). Interest rate option models: a critical survey.
  30. (1992). Interest rate volatility and the term structure: a two-factor general equilibrium model.
  31. (1975). Introduction to Mathematical Control Theory.
  32. (1996). Managing the volatility risk of portfolios of derivative securities: the lagrangian uncertain volatility model.
  33. (1997). Martingale Methods in Financial Modelling.
  34. (1984). Mathematical Methods for Wave Phenomena.
  35. (1997). Modelling Extremal Events.
  36. (1985). Numerical Solution of Partial Differential Equations: Finite Difference Methods. Oxford University Pres,
  37. (1994). Numerical Solution of Partial Differential Equations.
  38. (1978). On the term structure of interest rates.
  39. (1993). One-factor interest rate models and the valuation of interest rate derivative securities.
  40. (1991). Optimal Control: An Introduction to the Theory with Applications.
  41. (1993). Option Pricing: Mathematical Models and Computation.
  42. (1997). Options, Futures, and Other Derivatives.
  43. (1980). Partial Differential Equations. doi
  44. (1998). Pricing and hedging convertible bonds under non-probabilistic interest rates. OCIAM Working Paper,
  45. (1995). Pricing and hedging derivative securities in markets with uncertain volatilities.
  46. (1991). Pricing and Hedging Swaps.
  47. (1996). Pricing interest rate contingent claims in markets with uncertain volatilities. Courant Institute,
  48. (1990). Pricing interest-rate derivative securities.
  49. (1995). Spot-on modelling. Risk magazine,
  50. (1997). Static options replication. In Frontiers in Derivatives.
  51. (1994). Static simplicity. Risk magazine,
  52. (1996). Swap Literacy.
  53. (1994). Swaps and Financial Derivatives.
  54. (1986). Term structure movements and pricing interest rate contingent claims.
  55. (1992). The art of the optimum. In From Black-Scholes to black holes: new frontiers in options. Risk magazine / Finex,
  56. (1997). The market model of interest rate dynamics. doi
  57. (1995). The Mathematics of Financial Derivatives. doi
  58. (1976). The pricing of commodity contracts.
  59. (1973). The pricing of options and corporate liabilities. doi
  60. (1997). The yield envelope: price ranges for fixed income products.
  61. (1900). The´orie de la spe´culation. Annales Scientifiques de l’Ecole Normale Supe´rieure,
  62. (1995). Uncertain volatility and the risk-free synthesis of derivatives.
  63. (1997). Value at Risk.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.