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 ...
- 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 ...
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 ...
- 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 ...
- 51
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:
$$\Phi(...
- 7,091
3
votes
Accepted
CMS options, cash-settled/physically-settled swaptions
In a cash settled swaption the payoff is settled using the cash annuity contractually computed using the swap rate. Thus is you work out the replication procedure you will find that CMS replication is ...
- 5,532
3
votes
Girsanov theorem in CMS convexity derivation
Note that $$\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, ...
- 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
- 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
...
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 ...
- 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 ...
- 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} \...
- 5,532
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. ...
- 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 ...
- 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 ...
- 5,532
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 ...
- 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 ...
- 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}^...
- 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 ...
- 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 ...
- 11
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