Implementing the Hull and White (1994) interest rate model to price multi-callable bonds within the German banking market

This paper is a case study, documenting work completed for Institut fur betriebswirtschaftliche Beratung der Kreditwirtschaft GmbH1 (hence forth referred to as IFB) in Köln, Germany. The practicum involved the implementation of an interest rate model for the purpose of valuing the Multi-callable bond. The brief given was to develop a model that could be implemented into the software (Okular) to price the MCB in a fast and accurate way, so as to satisfy the regulatory body that oversees the supervision of the German banking industry. The model chosen to implement was the Hull and White model (1994) which first appeared in the literature in Hull and White (1990) and is often referred to as the modified Vasicek (1977). The 1994 model is developed further and is computationally more efficient. Interest rate models like Vasicek (1977) also appeared in the literature in Courtadon (1982) and Cox, Ingersoll, and Ross (1985). The approach of these models is to fit the market data and imply the yield curve and its evolutionary process. The Hull and White(1990) uses a different process. By taking the current yield curve as a given input, this model produces an arbitrage free yield curve that is consistent with the data. This style of model was seen first in Ho and Lee (1986), but the Hull and White (1994) is developed further to incorporate a mean reversion parameter and time dependent volatility term. In the Hull and White (1994), the trinomial tree process is manipulated to reproduce the stochastic process of the short rate with mean reversion. The tree is truncated to stop the evolution of negative interest rates, which have always bothered practitioners, and is also made computationally more efficient by this truncation process. One of the reasons this model was chosen is because of the vast amount of literature available on the implementation of this model, most notably Hull and White (1994), Numerical procedures for implementing term structure models I: single factor models, where the model in question is developed in such a way as to make it easy to implement for practitioners. Other notable papers for the implementation of this model are: Hull and White (1996). Using Hull-White interest-rate trees and Hull and White, (2000), the general Hull-White model and super calibration. Two texts were also instrumental in the implementation of this model: J.Hull, 1997, Options, Futures and Other Derivative Securities, 3rd edition and Les Clewlow and Chris Strickland, 1998, Implementing Derivatives Models. The following section gives a brief description of IFB. Section 3 looks at the German banking industry and offers some insights into a banking industry under reform. Section 4 looks at the model, dealing with the issues of the model brief, model selection and formal description. Section 5 deals with the implementation of this model and specifically with the process of taking the theory and developing it into a coded model. The process involved explaining the model in such a way that made it clear to programmers who had little or no financial knowledge, but were still required to develop the model in an object orientated computer language. This task was made more difficult by a language barrier. Section 6 deals with the issue of calibration, and a conculsion and appendix follow.UnpublishedAndrew Kalotay, George Williams, and Frank Fabozzi, A Model for Valuing Bonds and Embedded Options, Financial Analysts Journal, May/June 1993. Black, F., and P. Karasinski (1991). Bond option pricing when the short rates are lognormal, Finance Analysts J., 47(4), 52-59 Clewlow, L. and C. Strickland. Implementing Derivatives Models. Chichester, U. K.: Wiley (1998). Cox, J. C., J.E. Ingersoll, and S. Ross, (1981). The relation between forward prices and futures price, J. Financial Economics 9,321-346 Dempster P., Chaput J. Scott, Stent A.,(2002), A Comparison of Interest Rate Models on Australian Bank Bill Futures, Conference Paper, Department of Finance and Quantitative Analysis, University of Otago. Deutsche Bundesbank, Special Series, no. 2. Banking Act of the Federal Republic of Germany, (1996). Rudolf Panawitz & Harald Jung , Kreditwesengesetz-Banking Am. German-English Commentary (1988). Economist (1999), Survey of international Banking. Vol. 351/nr. 8115. Heath, D., R. Jarrow, and A. Morton, Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation. Journal of Financial and Quantitative Analysis 25 (1990), 419-440. Ho. T., and S. Lee, Term Structure Movements and Pricing Interest Rate Contingent Claims, Journal of Finance, December 1986, pp. 1011-29. Hull, J., Options, Futures, and Other Derivative Securities, 3rd Edition, Prentice Hall, 1997 Hull, J., and A. White, (1990). Pricing interest rate derivative securities, Rev. Financial Studies 3,573-592. Hull, J., and A. White, (1994). Numerical procedures for implementing term structure models I: single factor models, Journal of Derivatives, Fall, 7-16. Hull, J., and A. White, USING HULL-WHITE INTEREST-RATE TREES, (1996), Journal of Derivatives, Winter, 1996. Hull, J., and A. White, The General Hull-White Model and Super Calibration. (2000), Rotman School of Management, University of Toronto, Working Paper Lang, Gunter. The Impact of SMP and EMU on German Banking. Working paper , University of Augsburg Peisser, A., An efficient algorithm for calculating prices in the Hull-White model, ABNAmro Bank, Derivative Product Research and Development working paper, 1994. Smith, D., Techniques for Deriving a Zero Coupon Curve for Pricing Interest Rate Swaps: A Simplified Approach, The Handbook of Interest Rate Risk Management, Chapter 20, ed. J. C. Francis and A. Wolf, Irwin, 1994. Tian, T., A Modified Lattice Approach to Option Pricing, Journal of Futures Markets, Volume 13, Number 15, 1993, pp. 563-77. Vasicek, 0., (1977). An equilibrium characterization of the term structure, J. Financial Economics, 5, 177-188. Author unknown, The German Banking System, BankVerlag, Cologne/Germany (1999) Author unknown, US. Treasury Dept. Report, Modernising The Financial Systems: Recommendations for Safer, More Competitive Banks 54-61 (1991