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CMS Spread Single-Look Options and Shifted LMM Pricing

Article Quant Q&A · Author: Dan
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Summary

A single-look CMS spread option pays on the difference between two forward constant-maturity swap rates relative to a strike on one expiry date. A CMS spread cap or floor instead consists of options settling on multiple dates. Both structures can express a view on the yield curve’s shape.

The response says complex CMS spread options are often priced with a shifted Libor Market Model calibrated to at-the-money swaptions and quoted CMS spread options. The shift accommodates negative rates in a model where forward rates otherwise follow lognormal dynamics. The question also asks about strike shift, but the response does not establish what that term means; it offers the negative-rate model shift only as a guess. No pricing comparison, calibration example, or evidence about valuation accuracy is provided.

Key ideas

  • A single-look CMS spread option references the rate spread at one expiry date.
  • A CMS spread cap or floor comprises options with payments across multiple dates.
  • Both structures can provide exposure to changes in yield curve shape.
  • A shifted Libor Market Model may be calibrated to swaptions and CMS spread option quotes.
  • The response does not clarify whether strike shift means the shift used to accommodate negative rates.

Tags

Fixed incomeOptionsDerivatives pricing
Full text
# What is CMS Spread Option Single Look? In what ways is it different from CMS Spread Cap/floor?


# What is CMS Spread Option Single Look? In what ways is it different from CMS Spread Cap/floor?












What is CMS Spread Option Single Look? In what ways is it different from CMS Spread Cap/floor? Also, what's strike shift? What's its function in CMS spread options' pricing? Thanks.

## Answer by oronimbus (score 2)

https://quant.stackexchange.com/a/46876

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 and pays on each $t_i$ from $t_1$ to $t_n$. Both types are quoted by brokers such as Tullet. Both products allow the investor a view on the shape of the yield curve.

I'm not sure what you mean by strike shift though but I'll take a guess: Typically the pricing of such complex interest rate products (single or multi-look options) is done with a (Shifted) Libor Market Model (LMM), calibrated to both ATM swaptions of each tenor as well as the quoted, typically multi-look CMS spread options. Since the forward rates under LMM follow a log-normal distribution the market has been forced to apply a "shift" to accommodate for negative rates.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.