Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates
We derive a unified model which gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero-coupon bonds. The crucial assumption is that forward rates with a compounding period that matches the contract, which we want to price, is log-normally distributed. Moreover, this assumption is shown to be consistent with the Heath-Jarrow-Morton model for a specific choice of volatility.
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- 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.
- Rady, Sven, 1994. "The Direct Approach to Debt Option Pricing," Munich Reprints in Economics 3404, University of Munich, Department of Economics.
- K. Sandmann & Sandmann, K., 1995. "The Direct Approach to Debt Option Pricing," Discussion Paper Serie B 212, University of Bonn, Germany.
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