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Defining Spread Volatility for Treasury Futures Curve Trades

Article Quant Q&A · Author: Jay C
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Summary

The document describes a yield curve steepening or flattening position built from two year and ten year Treasury futures. The proposed steepener buys two shorter maturity contracts and sells one longer maturity contract, with the reverse position used for flattening. The question asks how to combine the stated contract volatilities to estimate volatility of the spread.

The response emphasizes that “expected volatility” must first be defined mathematically. The individual contract volatilities alone do not specify the spread’s volatility; a calculation also needs a precise spread return or P&L definition and the relationship between the legs, such as their covariance over the relevant horizon. The exchange does not provide a formula or numerical estimate, so the main lesson is to formalize the measure before attempting to aggregate risk.

Key ideas

  • A Treasury curve steepener can pair long shorter maturity futures with short longer maturity futures.
  • The flattening trade reverses the steepener’s futures positions.
  • Individual contract volatilities are insufficient to determine spread volatility.
  • The spread measure and the dependence between the futures legs must be specified before calculating risk.

Tags

FuturesFixed incomeVolatilityRisk management
Full text
# Yield curve steepening/flattening using different duration treasury futures (TUT Spread) and volatility


# Yield curve steepening/flattening using different duration treasury futures (TUT Spread) and volatility












Yield curve steepening: long 2 contracts 2 year (2 contracts due to contract size), short 1 contract 10 year Vice versa for flattening.

If the 2 year note has a expected volatility of 2% per contract (or 4% for 2 contracts) and the 10 year has a expected volatility of 6%, how can i calculate the expected volatility of this spread?

## Answer by Lech (score 0)

https://quant.stackexchange.com/a/67831

Firstly you need to define what you mean by "expected volatility". Once you formulate formally the expected volatility, then I presume you will get the answer yourself.

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