We reconstruct arbitrage free dynamics for the term structure of interest rates driven by infinitely many factors, each one representing a basic shape for the instantaneous forward rate curve in a given market. The consistency between a finite dimensional space of polynomials where the curve is day-to-day recovered and the proposed evolution equation is investigated. The main result is the developement of a historical-implicit hybrid calibration procedure for our infinite-dimensional shape factor model. In this context we also derive a pricing formula for caplets.
Theory and calibration of HJM with shape factors
GUIOTTO, PAOLO;
2002
Abstract
We reconstruct arbitrage free dynamics for the term structure of interest rates driven by infinitely many factors, each one representing a basic shape for the instantaneous forward rate curve in a given market. The consistency between a finite dimensional space of polynomials where the curve is day-to-day recovered and the proposed evolution equation is investigated. The main result is the developement of a historical-implicit hybrid calibration procedure for our infinite-dimensional shape factor model. In this context we also derive a pricing formula for caplets.
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