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Summary: A stochastic volatility model for callable CMS
swaps and translation invariant path dependent
derivatives
Claudio Albanesey
Manlio Trovatoz
May 22, 2006
Abstract
We present a stochastic volatility term structure model based on a
continuous time lattice which allows for a numerically stable and quite
e¢ cient methodology to price ...xed income exotics. We present numerical
applications to bermudan swaptions and callable CMS swaps. We then ex-
tend the model to translation invariant path dependent payo¤s by means
of an e¢ cient dimensional reduction technique and show its application
to callable range accruals and target redemption notes.
1 Introduction
The history of interest rate models is characterized by a long series of turns.
The Black formula for caplets and swaptions was designed to take as underlying
a single forward rate under the appropriate forward measure. This approach
has the advantage to lead to a simple pricing formula for European options but
also the limitation of not being extendable to callable contracts. To have a
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