Financial Modelling in Python

P1: JYS

c10 JWBK378-Fletcher May 12, 2009 19:2 Printer: Yet to come

10

Pricing Financial Structures

in Hull–White

In this chapter we bring everything we have developed in the preceding chapters together

and apply it to the pricing of a number of financial structures: namely Bermudans and target

redemption notes. The structures have been chosen for two reasons: firstly, they are fairly

straightforward; and, secondly, they demonstrate the need for both lattice and Monte-Carlo

pricing algorithms. For each trade type we begin by defining the structure before moving on

to the actual pricing. Test cases have been written for both trade types and are discussed in

detail in the following sections.

10.1 PRICING A BERMUDAN

In this section we illustrate how we can use the model components described in the pre-

ceding chapters to price a Bermudan swaption. First of all we need to understand what we

mean by a Bermudan swaption. A Bermudan swaption gives the holder the right to exer-

cise into an underlying vanilla swap at regular intervals. The underlying vanilla swap of a

Bermudan receiver swaption, is structured so that the holder, upon exercise, pays LIBOR

plus a spread in exchange for a fixed coupon at regular intervals until the end of the swap.

For a Bermudan payer swaption, the legs of the underlying vanilla swap are the other way

around.

The payoff class from module ppf.pricer.payoffs.fixed

leg payoff encap- ...