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Theta in P/L Estimates from Zero-Rate Curve Greeks

Article Quant Q&A · Author: thor
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Summary

The document asks whether a one-day P/L estimate based on sensitivity to a zero-rate curve includes the effect of time passing. The setup recalculates the curve on the next day using the same bonds, whose remaining maturities have shortened, and applies the original sensitivity to the change in the corresponding curve point.

The response says time-related P/L can be isolated by holding the other inputs constant and advancing time by one day. It cautions against calling this effect theta, since that term is commonly used for an option’s time decay. The short answer gives no worked calculation or discussion of curve construction, repricing assumptions, or how to separate time effects from market moves, so it offers a conceptual distinction rather than a full attribution procedure.

Key ideas

  • A zero-rate curve can change as time passes even when the underlying bonds are unchanged.
  • Time-related P/L can be estimated by holding inputs fixed and advancing the valuation date.
  • The response distinguishes general time P/L from theta, which it associates with option time decay.
  • The document does not provide a detailed numerical method for separating time effects from market changes.

Tags

Fixed incomeRisk management
Full text
# When estimating P/L through greeks based on zero rate curves, does it contain time (theta) PNL?


# When estimating P/L through greeks based on zero rate curves, does it contain time (theta) PNL?












Suppose on day 1 we calculate a delta wrt. a point on an interest curve of zero rates, we then let 1 day pass, recalculate the interest curve of zero rates with the same bonds (though now day 20 bond becomes day 19 etc.), we take the change in the risk factor (the difference in a point on the two risk factors matching the delta) and we estimate the PL for day 2.

Does our estimate contain P/L associated with time passing? what we might call theta or time PnL.

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/42390

Yes. The time p/l can be found by leaving all the inputs the same and allowing a day to pass. I prefer not to call it theta - that term is used to describe the time decay of options.

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