Interest Rate Derivatives in a Duffie and Kan Model with Stochastic Volatility: An Arrow-Debreu Pricing Approach |
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Authors: | Nunes João Pedro Vidal Clewlow Les Hodges Stewart |
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Affiliation: | (1) Warwick Business School, University of Warwick, U.K.;(2) CEMAF, Edif. INDEG/ISCTE, Av. Prof. Aníbal Bettencourt, 1600 Lisboa, Portugal;(3) Financial Options Research Centre, University of Warwick, U.K.;(4) School of Finance and Economics, University of Technology, Australia;(5) Centre for Financial Mathematics, Australian National University, Australia |
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Abstract: | Simple analytical pricing formulae have been derived, by different authors and for several derivatives, under the Gaussian Langetieg (1980) model. The purpose of this paper is to use such exact Gaussian solutions in order to obtain approximate analytical pricing formulas under the most general stochastic volatility specification of the Duffie and Kan (1996) model. Using Gaussian Arrow-Debreu state prices, first order stochastic volatility approximate pricing solutions will be derived only involving one integral with respect to the time-to-maturity of the contingent claim under valuation. Such approximations will be shown to be much faster than the existing exact numerical solutions, as well as accurate. |
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Keywords: | exponential-affine models stochastic volatility Arrow-Debreu prices bonds interest rate futures European path-independent interest rate options |
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