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http://ssrn.com/abstract=221951
 
 

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Interest Rate Derivatives in a Duffie and Kan Model with Stochastic Volatility: An Arrow-Debreu Pricing Approach


João Pedro Vidal Nunes


ISCTE Business School

Les Clewlow


Lacima; University of Warwick - Financial Options Research Centre (FORC); University of Technology Sydney (UTS) - School of Finance and Economics

Stewart D. Hodges


University of Warwick - Financial Options Research Centre (FORC)


Review of Derivatives Research, Vol. 3, Pp. 5-66, 1999

Abstract:     
Simple analytical pricing formulae have been derived, by different authors and for several interest rate contingent claims, 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 formulae under the most general stochastic volatility specification of the Duffie and Kan (1996) model, for several European-style interest rate derivatives, namely for: default-free bonds, FRAs, IRSs, short-term and long-term interest rate futures, European spot and futures options on zero-coupon bonds, interest rate caps and floors, European (conventional and pure) futures options on short-term interest rates, and even for European swaptions.
First, the functional form of an Arrow-Debreu price, under the Gaussian specification of the Duffie and Kan (1996) model, is obtained in a slightly more general form than the one given by Beaglehole and Tenney (1991). Then, and following Chen (1996), each stochastic volatility pricing solution is expressed in terms of one integral with respect to each one of the model's state variables, and another integral with respect to the time-to-maturity of the contingent claim under valuation. Finally, unlike in Chen (1996) and as the original contribution of this paper, all stochastic volatility closed form solutions are simplified into first order approximate pricing formulae that do not involve any integration with respect to the model's factors: only one time-integral is involved, irrespective of the model dimension. Consequently, such approximations will be shown to be much faster than the existing exact numerical solutions, as well as accurate. Moreover, asymptotic error bounds are provided for the proposed approximations.

JEL Classification: G132 G13, C63, E43

Accepted Paper Series


Not Available For Download

Date posted: April 18, 2000  

Suggested Citation

Nunes, João Pedro Vidal and Clewlow, Les and Hodges, Stewart D., Interest Rate Derivatives in a Duffie and Kan Model with Stochastic Volatility: An Arrow-Debreu Pricing Approach. Review of Derivatives Research, Vol. 3, Pp. 5-66, 1999. Available at SSRN: http://ssrn.com/abstract=221951

Contact Information

João Pedro Vidal Nunes (Contact Author)
ISCTE Business School ( email )
Ed. INDEG/ISCTE
Av. Prof. Anibal Bettencourt
Lisboa, 1600-189
Portugal
+351 21 790 39 32 (Phone)
+351 21 793 87 09 (Fax)
HOME PAGE: http://iscte.pt/~jpvn/
Les Clewlow
Lacima ( email )
London
United Kingdom
HOME PAGE: http://www.lacimagroup.com
University of Warwick - Financial Options Research Centre (FORC)
Coventry CV4 7AL
United Kingdom
HOME PAGE: http://www.wbs.ac.uk/expertise/research_teaching/f
University of Technology Sydney (UTS) - School of Finance and Economics ( email )
Haymarket
Sydney, NSW 2007
Australia
HOME PAGE: http://www.business.uts.edu.au/finance/
Stewart D. Hodges
University of Warwick - Financial Options Research Centre (FORC) ( email )
Warwick Business School
Coventry CV4 7AL
United Kingdom
01203-523606 (Phone)
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