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7

Here's a research note devoted to pricing of CMS by means of a stochastic volatility model. The authors indicate in the Introduction that an analysis of the coupon structure leads to the conclusion that CMS contracts are particularly sensitive to the asymptotic behavior of implied volatilities for very large strikes. Market CMS rates actually drive the ...


6

CMS adjustments in single curve context can be roughly explained if you consider a CMS swaplet by the fact that there is a single payment at the CMS rate at a single date and not on the whole strip of the underlying CMS tenor schedule. So if you are trying to hedge a CMS swaplet with the corresponding swap of CMS tenor length (with correct naïve nominal ...


4

The SABR model has an overly fat right tail. If you do the CMS replication using cash-settled swaptions you find that you need ridiculously high strikes.


1

In a vanilla swap, the IR on the floating leg usually depends on the reset period/swap frequency. If frequency is 6m, 6m LIBOR is used for reset, 3m LIBOR for quarterly resets etc. In a floating CMS leg, the rate used is the CMS rate, regardless of the reset frequency e.g: 10yr CMS leg will use the 10 yr CMS rate, regardless of whether the reset happens semi-...


1

In simple terms: An ordinary swap might be a 10 year swap of Libor vs a fixed rate; this fixed rate is determined in the marketplace every day and is published by Reuters, Bloomberg etc. as the '10 year swap rate'. Once you enter into the swap this rate remains fixed for you, of course, that is why it is called a fixed rate. But every day Reuters publishes a ...


1

A constant maturity swap (CMS) rate for a given tenor is referenced as a point on the Swap curve. A swap curve itself is a term structure wherein every point on the curve is the effective par swap rate for that tenor. This is analogous to a 3m LIBOR curve represents 3m forward rates for a given tenor. A swap rate can be considered as a weighted-average of ...


1

Note that $$\frac{dQ_{T_p}}{dQ}|_{T_0} = \frac{P(T_0, T_p)}{P(0, T_p)}\frac{A(0, T_0, T_n)}{A(T_0, T_0, T_n)}$$. Then $$E^{Q_{T_p}}\big(S(T_0, T_n)\big) = E^Q\bigg(S(T_0, T_n) \frac{P(T_0, T_p)}{P(0, T_p)}\frac{A(0, T_0, T_n)}{A(T_0, T_0, T_n)}\bigg) \\ = \frac{A(0, T_0, T_n)}{P(0, T_p)} E^Q\bigg(S(T_0, T_n) \frac{P(T_0, T_p)}{A(T_0, T_0, T_n)}\bigg).$$ That ...


1

A good place to start is Hagan's paper Convexity Conundrum ...available on the web.



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