# Questions tagged [cms]

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### What is the reason for the convexity adjustment when pricing a constant maturity swap (CMS)?

I'm trying to wrap my head around pricing a Constant Maturity Swap (CMS). Let's imagine the following deal: 6m LIBOR in one direction, 10y swap rate in the other. The discount curve is derived from ...
3k views

### Why is the SABR volatility model not good at pricing a constant maturity swap (CMS)?

I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that?
3k views

### What is the replicating portfolio of swaptions for a constant maturity swap (CMS)?

How do you replicate the payoff of a constant maturity swap rate? That is, if the payoff of a contract pays the 5-year swap rate every year for 10 years, how would you replicate this payoff using ...
405 views

### CMS Pricing - Convexity Adjustment by Replication [closed]

I'm trying to learn CMS pricing, but didn't get the logic of this method. Previously cited articles about this method is pretty complex. I'd be glad if you can provide me with simpler articles or ...
12k views

### What is a Constant Maturity Swap (CMS) rate?

I have been searching in books and on the internet for a basic definition and explanation of CMS rates, but I cannot find anything clear and simple. Can you explain (maybe with an example) what a CMS ...
73 views

### Constant Maturity Swap dates and conventions

Let's note $L(t,T_i,T_{i+1})$ the libor rate observed at $t$, fixing at $T_i$ with delivery at $T_{i+1}$. The natural delivery date for this rate is $T_{i+1}$, so a vanilla swap with no pay lag would ...
323 views

### Girsanov theorem in CMS convexity derivation

I am going through the derivation of CMS convexity from the notes of Lesniewski There is a transformation from $T_p$ forward measure to annuity measure $Q$ as  P(0,T_p)E^{Q_{T_p}}\left[S(T_0,T)\...
739 views

### CMS options, cash-settled/physically-settled swaptions

CMS options are traditionaly replicated using a theoritical "continuous" strip of swaptions (see for instance Hagan's paper "Convexity Conundrums : Pricing CMS Swaps, Caps and Floors"): In the paper,...
1k views

### duration of a cms swap

in the linked paper kwok_part2_exotic_swaps it says the following: A Swedish company has recently embraced the concept of duration and is keen to manage the duration of its debt portfolio. In the ...
557 views

### CMS spread vanilla options quotation

How are vanilla (call/put) options on CMS spread quoted on the markets ? Through an implied (normal/lognormal) volatility with a normal/lognormal model on the spread in the forward measure ?
97 views

### Are forward rates starting at observation date spot rates?

In part 3.2 of Lu and Neftci (2003) "Convexity Adjustments and Forward Libor Model: Case of Constant Maturity Swaps", the authors propose a new way of pricing CMS swaps, with Monte Carlo simulations. ...
676 views

### Where can I find CMS swap trading prices?

I am writing a paper about CMS swap. To do so, I'd like to compare different theoretical pricing methods of these instruments to the "real prices" i.e. prices used in the marketplace. But I don't ...
183 views

### Question on volatility equation for CMS pricing

In "Full implications of CMS convexity (Cedervall and Piterbarg, 2012)", a.k.a. "CMS: covering all bases (idem)", the authors develop a CMS model equipped with an annuity mapping function which ...
445 views

### Basis swap spread pricing and bootstrapping

Here is the expression of a basis floating versus floating swap where the first term is a forward CMS Swap leg and the second one is a forward BOR leg where X is the margin that would make equal both ...
50 views

### Vega for Constant Maturity Swaps

Why does a Constant Maturity Swap have a positive vega? Is it because of the convexity? How does one hedge it?