A model is presented for pricing European/Bermudan type callable capped floating rate note (FRN) swaps. The capped FRN swap is a contract to swap cash-flows between a vanilla floating rate leg and a capped floating rate leg. The option gives the right to call the swap back in favor of the option owner.
Pricing the capped FRN swap is relatively simple as the value can be expressed in a close-form analytical formula. To price the option with Bermudan type, the capped FRN swap has been reduced to a contract to swap cash-flows between a fixed leg and a caplet leg. To make the reduction valid, we need to assume that the date-setting in both legs of the capped FRN swap are almost consistent.
With the help of this simplification, each intrinsic value of the option is the one of a corresponding caption. Therefore, the option becomes Bermudan type caption. Under the model of a single-factor dynamics of a pseudo-forward rate, this caption an be priced by using the tree approach.
Let 1; 2 be index of cash-flow legs. Let Li (t) be a forward interest rate seen at a time of t for the forward accrual period.
It is clear to see that, on the right side of equation above, the first term is the value of the floating coupon, the second term is value of the ith caplet and the last term is the value of the ith floorlet. Coupon can be generated as https://finpricing.com/lib/FiBondCoupon.html
In this case, the Leg 2 is composed of vanilla cash-flows which is generated by floating rates with spreads and cash-flows in Leg 1 are capped floating rate with rates spreads.
Usually, the flat extrapolation may be applied to the range of [0; t0]. Then, we define a process L under a propriate measure.