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Webcast: The relationship between CMS and Swaptions

Speaker: Dr David Cox

To watch this webcast now, please fill-in your details below:

A course on this topic is available in London Time Zone, New York Time Zone and Singapore Time Zone

Webcast Agenda

  • CMS v IRS payoff
  • The convexity gap
  • CMS Caps and Floors and Swaptions
  • Plugging the convexity gap
  • The importance of smile

Learning Outcomes

  • Understand the differences and similarities between CMS and vanilla swaps
  • Learn how to replicate CMS with a portfolio of Swaptions
  • Understand the importance of correct modelling of volatility smile when valuing OTM Swaptions


1. Why do CMS and vanilla Interest Rate Swaps have different convexity?
A. Because the P/L of a swap depends on the DV01 and a rate change and the DV01 alters with the level of rates. While for CMS the payoff is dependent on the change in the swap rate and is not dependent on the swap’s DV01.

2. Why do I need to buy both out of the money payers and receivers to hedge a CMS position where I am short the market?
A. As rates sell off I make more profit on the CMS that the equivalent swap, so I need some extra income to be able to replicate the CMS position with a vanilla swap. Buying OTM payers provides this. As rates rally, I lose more on the Swap than the CMS, so I need extra income from the receivers to cover the difference.

3. Why can’t I use at the money (“ATM”) vol quotes from Bloomberg to price the swaptions needed to replicate a CMS?
A. Because the CMS replication is done with out of the money (“OTM”) swaptions and, if you are using a simple option pricing model, you have to change the volatility in line with the smile or skew to reflect the correct market price of the OTM options. A more modern approach, where a stochastic volatility model such as “SABR” is used, will enable the ATM and OTM swaptions to be priced consistently.

Thank you to those attendees who submitted their questions.

Download the 'CMS Replication with Swaptions' spreadsheet.

LFS offers the 2-day 'Interest Rate Derivatives 2: Structured Products' programme with Dr David Cox in London and remotely via LFS Live.

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