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World,

When pricing a CMS Spread Option the market practice consider the strike as relative to ATM or Absolute?

If I relate to the following paper page 70 the author refers to absolute strike

[1] Dhamo,E., On the Calibration of the SABR–Libor Market Model Correlations, University of Oxford, 2011

http://www1.maths.ox.ac.uk/system/files/legacy/12804/Dhamo_diss_sub_30.9.11_11.49_AMENDED_VERSION_FOR_PUBLISHING_add_note_to_that_effect.pdf

Alternatively the following author refers to them as relative page 20 2 Wong,M-K., A Correlation-sensitive Calibration of a Stochastic Volatility LIBOR Market Model, University of Oxford

http://eprints.maths.ox.ac.uk/1384/1/Man_Kuan_Wong_dissertation.pdf

This topic has necessarily an impact on the static replication of cms rates.

Any relevant idea?

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  • $\begingroup$ Absolute (e.g. CMS spread options quoted with strikes K = -25 bps to +150 bps), with also ATM straddle quoted. But I don't see how the quotation convention would have an impact on the CMS replication. Could you clarify ? $\endgroup$ – Antoine Conze Jun 20 '17 at 13:59
  • $\begingroup$ Hi Antoine, my understanding is that relative is ATM+/-K while absolute is K (fixed I mean) therefore the volatilities used in the static replication portfolio should be somehow different? No? $\endgroup$ – Bond007 Jun 20 '17 at 14:02
  • $\begingroup$ Hi Radom. CMS replication says CMS forward/caplet/floorlet is integral of replication function vs vanilla swaptions, hence static weighted sum of vanillas if you choose to use finite number of vanillas. CMS spread option requires CMS marginals (obtained from replication) and correlation, or at a minimum CMS forwards (from replication) and correlation, so no static replication there. $\endgroup$ – Antoine Conze Jun 20 '17 at 14:16
  • $\begingroup$ you misunderstood the question. let me clarify to retrieve the market price of cms spread option I am doing a full replication of strike so I compute cms swap rates to price theses instruments. I am doing as many replication as many strikes quotted in the market [mainly from -25bp to +150bp]. Then with the market price I am extracting the correlation skew that match this price. So reading this two papers my question is how to understand the strike range of the market cms spread options price [from -25bp to +150bp]? as relative to ATM or absolute? from the two papers I got a doubt $\endgroup$ – Bond007 Jun 20 '17 at 14:24
  • $\begingroup$ The CMS spread options quotations I use for calibration are absolute : strike -25 bps to +150 bps. The ATM straddle is also quoted. $\endgroup$ – Antoine Conze Jun 20 '17 at 14:35

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