Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1998-01-30
The Review of Financial Studies 14(1), 149-185 (January 2001)
Physics
Condensed Matter
Statistical Mechanics
29 pages, 3 figures, submitted to Review of Financial Studies
Scientific paper
This paper offers a new class of models of the term structure of interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, constrained in such a way as to keep the forward rate curve continuous. We term the process followed by the shocks to the forward curve ``stochastic strings'', and construct them as the solution to stochastic partial differential equations, that allow us to offer a variety of interesting parametrizations. The models can produce, with parsimony, any sort of correlation pattern among forward rates of different maturities. This feature makes the models consistent with any panel dataset of bond prices, not requiring the addition of error terms in econometric models. Interest rate options can easily be priced by simulation. However, options can only be perfectly hedged by trading in bonds of all maturities available.
Santa-Clara P.
Sornette Didier
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