Estimating Price Sensitivity with Finite Differences

Summary

The question asks whether short-window changes in bond yields can be approximated by dividing bond-futures returns by duration. The response does not derive that relationship or explain how duration maps a futures price move into a yield change. Instead, it offers a general numerical method for estimating sensitivity: calculate a position’s value at the current price, recalculate it after a small price change, and take the difference between the two values.

This finite-difference approach can provide a practical estimate of how value responds to a price input without deriving an analytical derivative. However, the reply is brief and does not apply the method to a bond future, specify the size of the price bump, or address contract conversion factors, deliverable baskets, convexity, or yield conventions. It therefore offers a general valuation technique rather than a complete answer about the proposed bond-futures and yield approximation.

Key ideas

• A finite difference estimates sensitivity by comparing values at the original price and a slightly changed price.
• The response recommends recalculating value directly instead of deriving a price derivative.
• The answer does not validate the proposed relationship between futures returns and yield changes.
• Bond-futures details such as deliverables and convexity are not addressed.

Tags

# Bond Future and Bond Yield relation


# Bond Future and Bond Yield relation












I recently read, that yield changes during a short time window can be approximated by dividing the returns of futures on the bond by its Duration. Has anybody heard this before and can shed some light on why this works?

## Answer by ThatDataGuy (score 2)

https://quant.stackexchange.com/a/67975

In general it's not a good idea to calculate some sort of delta and then use it to estimate price sensitivity. It's better to calculate

Value 1 @ price 1, then Value 2 @ price 1 + some small price diff

so that delta = Value 2 - Value 1

It's a lot less complicated that understanding how to derive a formula for 1st derivative wrt to price.

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