Approximate pricing of swaptions in affine and quadratic models |
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Authors: | Anna Maria Gambaro Ruggero Caldana Gianluca Fusai |
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Affiliation: | 1. Dipartimento di Statistica e Metodi Quantitativi, Università Milano Bicocca (DiSMeQ), Via Bicocca degli Arcimboldi 8, 20126Milano, Italy.;2. Accenture S.p.A., Via Maurizio Quadrio 17, 20154Milano, Italy.;3. Faculty of Finance, Cass Business School, City University, 106 Bunhill Row, London, EC1Y 8TZ, UK.;4. Dipartimento di Studi per l’Economia e l’Impresa, Università del Piemonte Orientale “A. Avogadro”, via E. Perrone 18, 28100Novara, Italy. |
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Abstract: | This paper proposes new bounds on the prices of European-style swaptions for affine and quadratic interest rate models. These bounds are computable whenever the joint characteristic function of the state variables is known. In particular, our lower bound involves the computation of a one-dimensional Fourier transform independently of the swap length. In addition, we control the error of our method by providing a new upper bound on swaption price that is applicable to all considered models. We test our bounds on different affine models and on a quadratic Gaussian model. We also apply our procedure to the multiple curve framework. The bounds are found to be accurate and computationally efficient. |
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Keywords: | Pricing Swaptions Affine quadratic models Fourier transform Bounds |
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