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Webcast: The relationship between CMS and Swaptions

Speaker: Dr David Cox

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

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


Q&A


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.

To find out more, click on the location links above or contact us at advisor@londonfs.com

Are you interested in running our public courses in-house? Contact our in-house team to discuss further.


Why travel? Many clients are already attending our courses from the convenience of their home or office with LFS's state-of-the-art remote learning platform: LFS Live