Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates

Posted: 18 Aug 1999

See all articles by Kristian R. Miltersen

Kristian R. Miltersen

Copenhagen Business School

Klaus Sandmann

University of Bonn - The Bonn Graduate School of Economics

Dieter Sondermann

University of Bonn - Institute of Statistics

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Date Written: March 1995

Abstract

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.

JEL Classification: G13

Suggested Citation

Miltersen, Kristian Risgaard and Sandmann, Klaus and Sondermann, Dieter, Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates (March 1995). Available at SSRN: https://ssrn.com/abstract=6106

Kristian Risgaard Miltersen

Copenhagen Business School ( email )

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

Klaus Sandmann (Contact Author)

University of Bonn - The Bonn Graduate School of Economics ( email )

Adenauerallee 24-26
Bonn, D-53113
Germany

Dieter Sondermann

University of Bonn - Institute of Statistics ( email )

Adenauerallee 24-26
53113 Bonn, 53113
Germany

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