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2008•Journal of Hangzhou Dianzi UniversityRequires access

Valuing an Interest Rate Spread Option under the Multi-factor HJM Framework

Shujin Li

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Abstract

This paper studies the problem of pricing a European option on the difference of the two interest rates, which is analogous to an option to exchange one asset for another. We derive a closed-form of pricing formula of an interest rate spread options under a multi-factor Heath-Jarrow-Morton (HJM) term structure framework, which shows that the introduction of the imperfect interest rates movements is essential for pricing such option, for which a single-factor model such as Ho and Lee (1985) model should not be applied.

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This paper studies the problem of pricing a European option on the difference of the two interest rates, which is analogous to an option to exchange one asset for another. We derive a closed-form of pricing formula of an interest rate spread options under a multi-factor Heath-Jarrow-Morton (HJM) term structure framework, which shows that the introduction of the imperfect interest rates movements is essential for pricing such option, for which a single-factor model such as Ho and Lee (1985) model should not be applied.

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Available abstract

This paper studies the problem of pricing a European option on the difference of the two interest rates, which is analogous to an option to exchange one asset for another. We derive a closed-form of pricing formula of an interest rate spread options under a multi-factor Heath-Jarrow-Morton (HJM) term structure framework, which shows that the introduction of the imperfect interest rates movements is essential for pricing such option, for which a single-factor model such as Ho and Lee (1985) model should not be applied.

Key concepts: Heath–Jarrow–Morton framework, Interest rate, Interest rate derivative, Valuation of options, Imperfect, Forward rate, Short-rate model, Monte Carlo methods for option pricing

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