Evaluation Of Exotic CMS Rate Derivatives Based On Change Of Numeraire And SMM

CMS rate defined and quoted by the International Swaps and Derivatives Association(ISDA), is widely used in the market as a reference interest rate index. In the recent years especially since the financial crisis, government in all countries often intervene in interest rate and the yield curve is changing frequently. Derivative, whose underlying is CMS rate, on the one hand could be a hedging tool of debt for cnterprize, on the other hand provide the opportunity for the institutional investors on investments in change of short and long term structure of interest rate. Therefore, CMS rate derivatives have developed rapidly and their forms have become increasingly complex.Because the theory of change of Numeraire can seek out the relation be-tween the rate itself and its forward through the measure transformation, it is usually applied in the interest rate derivative pricing. Besides, in SMM the CMS rate is lognornial martingale under the relative martingale measure and could be described by the only parameter-CMS rate volatility which is easily determined with the current market data. Hence, the above two theories for the CMS rate derivative pricing are extremely valuable. The second chapter in this article makes a brief introduction to these two theories and some basic interest rate products in the market.The third chapter focuses on three types of CMS exotic derivatives pricing analysis. Firstly, for Constant Maturity Swap, during the pricing process there will be two problems, one is measure transformation adjustment due to the change from ordinary measure to martingale measure relative to CMS rate, the other is time correction due to noncoincidence between the observation date and payment date of standard Constant Maturity Swap. We finally obtain the estimation of Convexity Adjustment part in the framework of Numeraire and Taylor Expansion. Secondly, as far as CMS Spread Option, because there is no explicit solu-tion when the strike is non-zero, a pricing formula described by the sensibility Greek similar to ordinary European option formula is obtained with the help of Conditioning Integral Method. In addition. although CMS rates of all terms in forward probability selected have no propriety of martingale, this article takes advantage of the Generalized SMM and estimates all drifts using each volatility.Filially, the CMS Spread Range Accrual Note can be divided into various contingent range digital options which could be priced as the sensibility of delayed paid CMS Spread Option with respect to strike. In order to use the CMS Spread Option Pricing Formula directly, time correction is required. In the simulations the impact of the range’s type and CMS rate volatility on the product price coincides with Market Rules. Some point that should be noted is that, for derivatives whose underlying is a basket of interest rate, one factor model tend to get a departure from ordinary value, so it is not usual to assume that the correlation is1.