Arbitrage-Free Interpolation in Models of Market Observable Interest Rates
Models which postulate lognormal dynamics for interest rates which are compounded according to market conventions, such as forward LIBOR or forward swap rates, can be constructed initially in a discrete tenor framework. Interpolating interest interest rates between maturities in the discrete tenor structure is equivalent to extending the model to continuous tenor. The present paper sets forth an alternative way of performing this extension; one which preserves the Markovian properties of the discrete tenor models and guarantees the positivity of all interpolated rates.
|Date of creation:||01 Dec 2001|
|Publication status:||Published as: Schlogl, E., 2002. "Arbitrage-Free Interpolation in Models of Market Observable Interest Rates", In: Sandmann, K., Schönbucher, P. (eds.) Advances in Finance and Stochastics, 187-218.|
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- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Erik Schlögl, 2002.
"A multicurrency extension of the lognormal interest rate Market Models,"
Finance and Stochastics,
Springer, vol. 6(2), pages 173-196.
- Erik Schlögl, 1999. "A Multicurrency Extension of the Lognormal Interest Rate Market Models," Research Paper Series 20, Quantitative Finance Research Centre, University of Technology, Sydney.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
- David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
- Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- Sven Rady, 1997. "Option pricing in the presence of natural boundaries and a quadratic diffusion term (*)," Finance and Stochastics, Springer, vol. 1(4), pages 331-344.
- Sandmann,Klaus & Sondermann,Dieter, "undated". "A term structure model and the pricing of interest rate options," Discussion Paper Serie B 129, University of Bonn, Germany.
- Tim Dunn & Erik Schlögl & Geoff Barton, 2000. "Simulated Swaption Delta-Hedging in the Lognormal Forward Libor Model," Research Paper Series 40, Quantitative Finance Research Centre, University of Technology, Sydney.
- Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December. Full references (including those not matched with items on IDEAS)