Hot answers tagged

7 votes

CMS Pricing - Convexity Adjustment by Replication

The CMS represents the value of a swap rate for any point in time, i.e. we are interested in extrapolating the density of the swap rate in a similar way as the IBOR rate. Let us start with the fair ...
user avatar
  • 1,002
7 votes
Accepted

What is a Constant Maturity Swap (CMS) rate?

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 ...
user avatar
6 votes

What is a Constant Maturity Swap (CMS) rate?

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 ...
user avatar
  • 9,077
5 votes

What is a Constant Maturity Swap (CMS) rate?

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 ...
user avatar
3 votes

Constant Maturity Swap dates and conventions

To lighten notation, we assume a constant accrual factor $\tau$, a swap rate $S_n(T)$ which fixes at $T$ and pays at $T_p$ (e.g. $T_p-T=\text{3 months}$) and a simple CMS payoff of the form: $$\Phi(...
user avatar
3 votes
Accepted

CMS options, cash-settled/physically-settled swaptions

In a cash settled swaption the payoff is settled using the cash annuity contractually computed using the swap rate. Thus is you work out the replication procedure you will find that CMS replication is ...
user avatar
3 votes

Girsanov theorem in CMS convexity derivation

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, ...
user avatar
  • 20.4k
3 votes

Where can I find CMS swap trading prices?

The spread are quoted on ICAP or in Bloomberg if you have acess to them or you can refer to the paper of Mercurio where you have some quotes and examples
user avatar
  • 83
2 votes
Accepted

Where can I find CMS swap trading prices?

From On Valuing Constant Maturity Swap Spread Derivatives "The CMS tickers are represented as USSWAPyy, where yy is the year indicator. For Example the tickers for CMS 30 yrs and CMS 2 yrs are ...
user avatar
2 votes

CMS Valuation methods

Let $S_t$ the swap-rate and $A_t$ the associated annuity. You said that the convexity adjustment requires an annuity mapping function. That kind of approach is equivalent to calculate the following ...
user avatar
  • 753
2 votes

What is CMS Spread Option Single Look? In what ways is it different from CMS Spread Cap/floor?

A single look CMS spread option is simply an option on the difference between the two forward CMS rates and a chosen strike $K$ on a single expiry date $t$. A CMS spread cap is then a strip of options ...
user avatar
  • 775
2 votes
Accepted

Question on volatility equation for CMS pricing

Let $X_i(t) = 1+\delta_i S_i(t)$. Then $\nu_i$ is the log normal volatility for $X_i(t)$, and because $dX_i(t) = \color{blue}{\delta_i} dS_i(t)$ we get $\nu_i X_i(t) dW_t = \color{blue}{\delta_i} \...
user avatar
2 votes

CMS spread vanilla options quotation

Here is a quotation from an interbank broker last week: 1Y 2-10 Str 26-27. This means that a one year at the money straddle on the (10yr cms - 2 yr cms) has a spot price of 0.26% bid, 0.27% offered. ...
user avatar
  • 13.7k
2 votes

duration of a cms swap

Your intuition is correct and the paper seems to misunderstand the exposure of a swap based on CMS. The term "Constant Maturity Swap" or CMS, refers to the name of an index (the prevailing swap rate ...
user avatar
  • 13.7k
2 votes
Accepted

CMS convexity adjustment in a range accrual Monte Carlo

If you have done your simulation under the payment date forward measure then you only need to take the expectation of the indicator of the swap rate being between $K_1$ and $K_2$. If you have done ...
user avatar
1 vote

Cap/Floor on a SpreadOption grid

Not sure exactly how your data looks but you should be able to distinguish whether you have a cap or a floor depending on how the instrument is reacting to increasing and decreasing rates (forwards in ...
user avatar
  • 5,010
1 vote

duration of a cms swap

The cash flows on CMS leg reset based on some index, let's say the 5y swap rate. Duration measures sensitivity to different parts of the yield curve. The amount paid is based on that rate as of the ...
user avatar
  • 741
1 vote
Accepted

Basis swap spread pricing and bootstrapping

As far as I can tell, not being an expert in basis swap pricing, this is just algebra - $$ X_{n,c} = \frac{\sum_{i=1}^n \left( S_{i,c}'(0) + {\rm\bf CA}(S_{i,c}'; \delta)\right) P(0,T_i')}{\sum_{i=1}^...
user avatar
  • 5,603
1 vote

Where can I find CMS swap trading prices?

The question is about the prices of CMS swaps, which are swaps where one side pays CMS and the other side pays Libor + X, where X is the price we are looking for. The payment frequency is usually ...
user avatar
  • 13.7k
1 vote

What is a Constant Maturity Swap (CMS) rate?

The other answers explain the structure but they do not appear to address your follow up questions in the comments regarding the naming of a constant maturity swap (CMS). While it is true that the ...
user avatar

Only top scored, non community-wiki answers of a minimum length are eligible