Post by Sapphire Capital on Aug 7, 2008 23:15:56 GMT 4
The CARMA Interest Rate Model
Fred Espen Benth
CMA, University of Oslo - Department of Mathematics
Steen Koekebakker
Agder University College
Valeri Zakamouline
University of Agder - Faculty of Economics
November 22, 2007
Abstract:
In this paper we propose a continuous time autoregressive moving-average model (CARMA) for interest rate modeling. Our model generalizes Vasicek's interest rate model by allowing for higher order autoregressive and moving average terms in the interest rate dynamics. We provide closed-form solutions for bond and bond option prices. Despite the fact that the instantaneous short rate is driven by a single Brownian motion, it allows for surprisingly complex yield and volatility term structures. In particular, our model easily captures the humped shape volatility seen in fixed income markets. We demonstrate the capabilities of our model by calibrating to UK term structure data.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1138632_code356177.pdf?abstractid=1138632&mirid=2
Fred Espen Benth
CMA, University of Oslo - Department of Mathematics
Steen Koekebakker
Agder University College
Valeri Zakamouline
University of Agder - Faculty of Economics
November 22, 2007
Abstract:
In this paper we propose a continuous time autoregressive moving-average model (CARMA) for interest rate modeling. Our model generalizes Vasicek's interest rate model by allowing for higher order autoregressive and moving average terms in the interest rate dynamics. We provide closed-form solutions for bond and bond option prices. Despite the fact that the instantaneous short rate is driven by a single Brownian motion, it allows for surprisingly complex yield and volatility term structures. In particular, our model easily captures the humped shape volatility seen in fixed income markets. We demonstrate the capabilities of our model by calibrating to UK term structure data.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1138632_code356177.pdf?abstractid=1138632&mirid=2