A Constant Maturity Swap (CMS) derivative is an interest rate instrument whose payoff depends on a swap rate of a constant (fixed) maturity. The CMS derivatives provide a market efficient access to long dated interest rates (back end of the yield curve). In this thesis, the hedging and pricing of CMS derivatives are investigated. Various convexity adjustment methods have been proposed in the literature to adjust for convexity in forward CMS rates. In the first part, I consider the relation between replication of a CMS caplet using swaptions of varying strikes with convexity correction of the CMS caplet. I analyze the mathematical assumptions on the bond prices that are required for the success in the implementation of both the discrete and continuous replication, in particular, the prop...[ Read more ]

A Constant Maturity Swap (CMS) derivative is an interest rate instrument whose payoff depends on a swap rate of a constant (fixed) maturity. The CMS derivatives provide a market efficient access to long dated interest rates (back end of the yield curve). In this thesis, the hedging and pricing of CMS derivatives are investigated. Various convexity adjustment methods have been proposed in the literature to adjust for convexity in forward CMS rates. In the first part, I consider the relation between replication of a CMS caplet using swaptions of varying strikes with convexity correction of the CMS caplet. I analyze the mathematical assumptions on the bond prices that are required for the success in the implementation of both the discrete and continuous replication, in particular, the proper functional dependence of the bond-annuity ratio in terms of the CMS rates. I propose several modifications on dealing with CMS convexity adjustment. In the second part, I propose a log-normal co-initial swap market model and apply the model to price the CMS spread options. Pricing properties of various CMS spread options are investigated.