This paper studies the pricing of options whose payoffs are contingent on Constant Maturity Credit Default Swap (CMCDS) spreads. It extends the convexity adjustment method for Constant Maturity Swap (CMS) in interest rates by modeling the swap rate and CDS spread either as a single factor (a sum of the two) or as two factors separately. For the latter, the paper explicitly models the correlation between interest rate and credit spread in deriving the results. It is shown that when swap rate and CDS spread are independent of each other and when the yield curve is relatively flat, the two-factor model gives the same convexity adjustment as the one-factor model. Under lognormality assumptions, the model can produce analytic solutions for convexity adjustments as well as for the valuation of CMCDS derivatives such as CDS swaptions, caps and floors, and digital options.

Similar to Constant Maturity Swap (CMS) in interest rates, Constant Maturity Credit Default Swap (CMCDS) refers to a credit default swap where each premium payment is indexed to the market spread of a CDS with constant tenor (maturity). The premium rate (or CDS spread) is not known until the index (CDS spread) settles. For example, in a 10-year CMCDS indexed to a constant maturity of five years, the premium rates (5-year CDS spreads) form a time series that tracks the cost of buying 5-year default protection over the next 10 years.

In a CMCDS contract, each CDS spread is applied only to one premium payment which can be viewed as the first premium in a forward CDS contract. However, in a forward-starting CDS contract, the CDS spread is applied to all future premium payment periods. The valuation of the `first' premium in isolation is much more difficult than that of all the premiums as a whole. This is because the premiums at the CMCDS rate are earned over the entire term of the CDS contract. There is a timing mismatch. A simple example of such a mismatch is the LIBOR-in-arrears swap studied by Li and Raghavan (1996).

Derivatives Market Journal, Constant Maturity Credit Default Swap, CMCDS, Constant Maturity Swap, Brownian Motion, Convexity Adjustment Models, Credit Default Swaptions, Multiperiod Securities Markets, Financial Economics, Convexity Conundrums, Commodity Contracts.