How to Implement Market Models Using VBA

CHAPTER 8

Interest Rate Exotics

Interest rate exotics are a class of tailor-made interest rate-related assets that cover a wide range of payoffs. To investigate this area exhaustively would necessitate devoting a complete volume to the subject. In this section, we shall develop three popular payoffs, which over time have become “standard” instruments: CMS swaps, cancelable swaps, and one of the many versions of Target Redemption Notes. This will give us the opportunity to put theory into practice. To price the CMS and cancelable swaps, we will use two different models and share the results obtained from them. The TARN will be valued under the HJM model, with and without the help of factor reduction techniques (PCA).

8.1 CMS SWAPS

In the interbank market, reference rates are basically classified in three categories:

• overnight rates (e.g., EONIA), included in the calculation of short-term swaps;
• monetary rates, ranging from 1 month to 1 year in duration, such as the LIBOR benchmark;
• longer term rates, such as swap rates, generally named Constant Maturity Swap, with durations of more than 2 years.

The CMS reference generates a new class of derivatives:

• In a vanilla IRS, the benchmark floating rate payment frequency must comply with the period referenced: a 6-mth LIBOR is to be paid semi-annually.
• In a CMS swap, the floating reference, which is a long-term reference rate, is generally paid annually, which induces a convexity effect.

In fact, the only way to hedge a CMS swap is ...