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Using the Black-Derman-Toy interest rate model for portfolio optimization

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  • Weissensteiner, Alex

Abstract

No-arbitrage interest rate models are designed to be consistent with the current term structure of interest rates. The diffusion of the interest rates is often approximated with a tree, in which the scenario-dependent fair price of any security is calculated as the present value of the risk-neutral expectation by backward induction. To use this tree in a portfolio optimization context it is necessary to account for the so-called "market price of risk". In this paper we present a method to change the conditional probabilities in the Black-Derman-Toy model to the physical (or real) measure, including the market price of risk, and explore the economic implications for expected spot rates and for expected bond returns.

Suggested Citation

  • Weissensteiner, Alex, 2010. "Using the Black-Derman-Toy interest rate model for portfolio optimization," European Journal of Operational Research, Elsevier, vol. 202(1), pages 175-181, April.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:1:p:175-181
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    1. Rasmussen, Kourosh Marjani & Clausen, Jens, 2007. "Mortgage loan portfolio optimization using multi-stage stochastic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 742-766, March.
    2. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Jobst, Norbert J. & Zenios, Stavros A., 2005. "On the simulation of portfolios of interest rate and credit risk sensitive securities," European Journal of Operational Research, Elsevier, vol. 161(2), pages 298-324, March.
    4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1981. "A Re-examination of Traditional Hypotheses about the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 36(4), pages 769-799, September.
    5. M. A. H. Dempster & M. Germano & E. A. Medova & M. I. Rietbergen & F. Sandrini & M. Scrowston, 2007. "Designing minimum guaranteed return funds," Quantitative Finance, Taylor & Francis Journals, vol. 7(2), pages 245-256.
    6. John M. Mulvey & Stavros A. Zenios, 1994. "Capturing the Correlations of Fixed-income Instruments," Management Science, INFORMS, vol. 40(10), pages 1329-1342, October.
    7. Jobst, Norbert J. & Mitra, Gautam & Zenios, Stavros A., 2006. "Integrating market and credit risk: A simulation and optimisation perspective," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 717-742, February.
    8. John H. Cochrane & Monika Piazzesi, 2005. "Bond Risk Premia," American Economic Review, American Economic Association, vol. 95(1), pages 138-160, March.
    9. Dupacova, Jitka & Bertocchi, Marida, 2001. "From data to model and back to data: A bond portfolio management problem," European Journal of Operational Research, Elsevier, vol. 134(2), pages 261-278, October.
    10. Marida Bertocchi & Vittorio Moriggia & Jitka Dupačová, 2006. "Horizon and stages in applications of stochastic programming in finance," Annals of Operations Research, Springer, vol. 142(1), pages 63-78, February.
    11. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "Pricing options on scenario trees," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 283-298, February.
    12. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    13. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    14. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," Serie Research Memoranda 0011, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    15. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," European Journal of Operational Research, Elsevier, vol. 101(2), pages 374-392, September.
    16. Golub, Bennett & Holmer, Martin & McKendall, Raymond & Pohlman, Lawrence & Zenios, Stavros A., 1995. "A stochastic programming model for money management," European Journal of Operational Research, Elsevier, vol. 85(2), pages 282-296, September.
    17. Bernaschi, M. & Torosantucci, L. & Uboldi, A., 2007. "Empirical evaluation of the market price of risk using the CIR model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 543-554.
    18. Stanton, Richard, 1997. "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
    19. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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