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Interest Rate Theory (Financial Mathematics II)

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Interest Rate Theory (Financial Mathematics II)


Welcome! Here you find the latest information and material for the course Interest Rate Theory (Financial Mathematics II).


General Information

In this lecture we will study the "big brother" of the stock market: the fixed income or interest rate market. In particular, we will study

  • Fixed Income Products

  • Short Rate Models

  • The Heath-Jarrow-Morton Framework

  • The Change of Numéraire Technique

  • LIBOR and Swap Market Models

  • ... and, time permitting, lots more exciting stuff.


There is one lecture per week on 

  • Monday at 11.45 in 48-582.


Course Material

The current version of the lecture notes can be downloaded here. Please do not hesitate to contact us if you have any questions, suggestions or corrections.

The lecture notes also contain voluntary exercises and two appendices on short rate modeling under P and monotone class theorems.

The lecture notes for Stochastic Processes and Financial Markets (Financial Mathematics I) are available here.

The Excel sheet with simulations of various short rate models can be downloaded here.

The Excel sheets containing the yield curve evolution and the calibration of the Vasicek model are here and here.



The original articles referred to in the lecture can be downloaded here.

Björk, T.: A Geometric View of Interest Rate Theory, in Option Pricing, Interest Rates and Risk Management, Cambridge University Press (2001).

Black, F., Derman, E., Toy, W.: A One-Factor Model of Interest Rates and its Application to Treasury Bond Options, Financial Analysts Journal 46 (1990), 33-39.

Black, F., Karasinski, P.: Bond and Option Pricing When Short Rates Are Lognormal, Financial Analysts Journal 47 (1991), 52-59.

Black, F., Scholes, M.: The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81 (1973), 637-654.

Black, F.: The Pricing of Commodity Contracts, Journal of Financial Economics 3 (1976), 167-179.

Cheyette, O.: Markov Representation of the Heath-Jarrow-Morton Model, SSRN working paper (1995).

Cox, J., Ingersoll, J., Ross, S.: A Theory of the Term Structure of Interest Rates, Econometrica 53 (1985), 385-408.

Delbaen, F., Schachermayer, W.: A General Version of the Fundamental Theorem of Asset Pricing, Mathematische Annalen 300 (1994), 463-520.

Dothan, L.: On the Term Structure of Interest Rates, Journal of Financial Economics 6 (1978), 59-69.

Duffie, D., Kan, R.: A Yield-Factor Model of Interest Rates, Mathematical Finance 6 (1996), 379-406.

Flesaker, B., Hughston, L.: Positive Interest, Risk Magazine 9 (1996), 46-49.

Geman, H., El Karoui, N., Rochet, J.: Changes of Numéraire, Changes of Probability Measure and Option Pricing, Journal of Applied Probability 32 (1995), 443-458.

Heath, D., Jarrow, R., Morton, A.: Bond Pricing and the Term Structure of Interest Rates, Econometrica 60 (1992), 77-106.

Ho, T., Lee, S.: Term Structure Movements and Pricing Interest Rate Contingent Claims, Journal of Finance 41 (1986), 1011-1029.

Hull, J., White, A.: Pricing Interest-Rate-Derivative Securities, Review of Financial Studies 3 (1990), 573-592.

Keller-Ressel, M., Steiner, T.: Yield Curve Shapes and the Asymptotic Short Rate Distribution in Affine One-Factor Models, Finance and Stochastics 12 (2008), 149-172.

Longstaff, F., Schwartz, E.: Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model, Journal of Finance 47 (1992), 1259-1282.

Miltersen, K., Sandmann, K, Sondermann, D.: Closed Form Solutions for Term Structure Derivatives with Log-Normal Short Rates, Journal of Finance 52 (1997), 409-430.

Ritchken, P., Sankarasubramanian, L.: Volatility Structures of Forward Rates and the Dynamics of the Term Structure, Mathematical Finance 5 (1995), 55-72.

Rogers, C.:The Potential Approach to the Term Structure of Interest Rates, Mathematical Finance 7 (1994), 157-176.

Shiryaev, A., Cherny, A.: Vector Stochastic Integrals and the Fundamental Theorems of Asset Pricing, Proceedings of the Steklov Mathematical Institute 237 (2002), 12-56.

Vasicek, O.: An Equilibrium Characterization of the Term Structure, Journal of Financial Economics 5 (1977), 177-188.