Attributing Gamma PnL Across Hedging Intervals

Summary

The note asks how to divide a one-day gamma profit and loss across hourly price moves when the underlying rises steadily. It explains that the familiar one-period approximation, one-half gamma times the squared price change, does not by itself specify a unique hourly attribution. The answer distinguishes this accounting question from the total gamma PnL calculation.

Attribution depends on how often the portfolio is hedged and how delta gains that accumulate through gamma are recorded. The suggested convention is to choose a reporting frequency and apply it consistently, ideally matching the actual hedging frequency. The discussion offers no numerical hourly breakdown and does not work through alternative accounting schemes. Its main limitation is that attribution can vary with the chosen hedge and reporting convention, so the result should not be treated as a unique decomposition independent of trading practice.

Key ideas

• The one-period gamma approximation does not uniquely determine hourly PnL attribution.
• Delta PnL accumulated between hedges is also related to gamma.
• Choose and consistently apply an attribution frequency that reflects the portfolio's hedging frequency.

Tags

# Breaking down gamma PnL by time


# Breaking down gamma PnL by time












Let's say in one day time, underlying price S goes up by $2.4. Then the gamma PnL should be

$\frac{1}{2}\gamma_0 (2.4)^2$. Let's assume that in every hour the underlying goes up by $0.1. Then how do we breakdown this gamma PnL by hour? Or how much gamma PnL are we making every hour?

## Answer by volquant (score 1, accepted)

https://quant.stackexchange.com/a/78129

Unless you are hedging your portfolio fully every hour, there are mutliple ways to attribute gamma PnL here, all of them are correct and incorrect at the same time. Your delta PnL is also coming from gamma since the deltas you accumulate is a consequence of gamma (ignoring other second order spot Greeks). Just decide on a frequency you want to report the Greek PnL at and keep it consistent that way. Best way is to keep it a function of your hedging frequency.

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