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Double CMS Option A double CMS derivatives represents a European type derivatives whose matured payoff depends on two CMS rates.1 For most important products in the fixed income market, the payoff function can be an affine-linear with respect to two CMS rates and may be possibly capped and/or floored. Further, if the weighting-coefficients in the affine linear function, which are also called index gearing factors, have same signs, then it is also called (double-) CMS average; otherwise, it is called (double-) CMS spread. Conventionally, for the second and third types of payoffs, they may be called CMS average/spread call and put, respectively. One may also notice that a vanilla digital call (put) can be well approximated by two calls (puts). Hence a CMS average/spread digital call/put can be replicated by CMS average/spread calls/puts. In this vetting report, we only consider double-CMS derivatives with payoffs of type (b) and (c). Special examples are CMS spread calls (or cap or caplets), puts (or floor or floorlets) and swaps. A double-CMS (structured) swap is a swap contract with a regular funding leg and a structured (or CMS) leg in which coupons are functions of two CMS rates as mentioned above. Particularly, each (structured) coupon rate can be a sum of an affine-linear function with respect to two CMS rates and a linear combination of CMS average/spread calls and puts. With this structure, we have the following special cases: (a) simple CMS average/spread swaps in which coupon rates in the CMS leg are not capped nor floored, (b) CMS average/spread cap-floor swaps and (c) CMS average/spread digital swaps. The double-CMS swaps, which are considered in this vetting report, are not callable. With the above analysis and the restriction and also due to the additivity of the double-CMS products considered in this report, it suffices to discuss European CMS average/spread calls and puts. The SABRN model for European vanilla option together with a normal copula function approach is applied to determine the joint distribution of two terminal CMS rates. BMA Swap |