Modelling of CMS-Linked Products in an RFR framework, with Extension to Hybrids, Forward Starting and Canary Options
22 Pages Posted: 21 Jun 2022 Last revised: 24 Jun 2022
Date Written: June 17, 2022
Capitalizing on the Market’s adoption of Risk Free Rates (RFR) as benchmarks, we solve the problem of handling consistently single-expiry Interest Rates derivatives (e.g. CMS, CMS Spread-Options, Mid-Curves, Basket-Options etc..) in a way that respects the underlying swaps inter-dependencies as well as their volatilities across strikes and tenors, without resorting to arbitrary approximations routinely used in the industry. Introducing the convenient Annuity Due measure, we first show that the T-forward joint distribution of a family of RFR Swap Rates may be inferred explicitly from their options prices and correlation structure; we then design a numerical algorithm that allows the pricing of products sharing the same expiry using an efficient 1-step Monte Carlo scheme. Finally, we show how hybrid products involving e.g. Foreign Exchange or Equity may be similarly covered and propose an extension to 2-expiry instruments such as Forward Starting Swaptions or 2-expiry Bermudan (Canary Swaption).
Keywords: Swaptions, CMS, CMS Options, CMS Spread-Options, Forward Smile, Canary Options, LIBOR Reform
JEL Classification: C02, G13
Suggested Citation: Suggested Citation