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Pricing caps and floors with the extended CIR model

Antonio Mannolini, Carlo Mari and Roberto Renò
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Antonio Mannolini: Dipartimento di Economia Politica, Università di Siena, Italy, Postal: Dipartimento di Economia Politica, Università di Siena, Italy
Carlo Mari: Dipartimento di Metodi Quantitativi e Teoria Economica, Università di Chieti-Pescara, Italy, Postal: Dipartimento di Metodi Quantitativi e Teoria Economica, Università di Chieti-Pescara, Italy
Roberto Renò: Dipartimento di Economia Politica, Università di Siena, Italy, Postal: Dipartimento di Economia Politica, Università di Siena, Italy

International Journal of Finance & Economics, 2008, vol. 13, issue 4, 386-400

Abstract: We use the extended CIR model to value interest rate caps and floors. The extension allows arbitrary initial term structure, in the spirit of Hull and White, a crucial feature since we show that the pricing of the considered contingent claims improves dramatically after taking into account the big stake of market information contained in the yield curve. We compute model prices of at the money caps using only yield curve data, and we compare prices with those obtained when other well-known short-rate models are used, including the extended Vasicek model. With respect to natural benchmarks, we find a significant decrease in the pricing error for longer maturity caps when our model is used. These results witness that when a better specification of the dynamics of spot rate is provided, a satisfactory pricing of caps and floors is possible using only the information available in the bond market. Copyright © 2008 John Wiley & Sons, Ltd.

Date: 2008
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