The underlying security of a Bermudan swaption is an interest-rate swap, which is specified by respective payer and receiver legs. Each of the legs above can pay a fixed rate, Libor or CMS rate. The owner of the Bermudan swaption can choose to enter into the swap above at certain pre-defined exercise times.
Upon exercise, the owner of the Bermudan swaption must pay all payer-leg quantities that reset on or after the exercise time, and also will receive all receiver-leg quantities that reset on or after the exercise time.
We use Jamshidian’s Libor rate model where Libor rates are modeled simultaneously under the spot Libor measure. Furthermore we value a Bermudan swaption based on the Monte Carlo technique presented by Longstaff and Schwartz towards American style pricing. In particular, at every exercise time, we must solve a linear least squares problem, and then decide whether to exercise the option.
Below we examine the pricing of a Bermudan option to enter a swap that exchanges a yearly CMS rate, paid annually, for a semi-annual CMS rate, paid semi-annually. In particular we consider a Libor rate model specified by a set of quarterly reset points.
We calibrate the Jamshidian model parameters based on a portfolio of European style CMS rate options with payoff of the form. In particular we consider a portfolio consisting of options on the payer leg CMS rate, with maturity at each annual reset time, from the one year point up to and including the eight year point, and also options on the receiver leg CMS rate, with maturity at each semi-annual reset time.
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