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Option and Hedge Mark-to-Market PnL in Delta Hedging

Article Quant Q&A · Author: babaji
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Summary

The document poses a foreign exchange delta hedging example involving a long USD/IDR straddle, an intraday currency move, and a new one-year non-deliverable forward used to rebalance delta. The hedge is traded at a bid or ask price, so the question asks how to combine risk-sensitivity-based profit and loss with trading costs.

The response gives only a general accounting principle: total profit and loss is the mark-to-market profit and loss of both the option position and its hedge. It does not show how to calculate the option’s gamma contribution, the forward’s mark-to-market change, or the spread cost, nor does it resolve which side of the market applies. Thus, it establishes that the hedge must be included in the portfolio-level PnL, but leaves the numerical calculation and transaction-cost treatment unspecified.

Key ideas

  • Portfolio PnL should include the mark-to-market change of both the option and its hedge.
  • The example uses an NDF trade to rebalance delta after an intraday currency move.
  • The response does not detail how to calculate gamma PnL or the hedge’s spread cost.
  • The direction of the hedge trade determines whether the bid or ask is relevant, but the answer does not specify it.

Tags

ForexOptionsDerivatives pricingRisk management
Full text
# Delta hedging/Gamma PnL


# Delta hedging/Gamma PnL












Suppose I am long USDIDR straddle with my start of the day delta being USD10m long IDR and USDIDR gamma being $5m.

There is a 1% intra-day IDR strengthening, so my delta becomes roughly long IDR 15m. I execute a 15m long USDIDR 1Y NDF to re-balance my delta (bid/ask spread 20 fwd points, 1Y USDIDR NDF mid 14850).

How do I calculate total risk sensitivities based PnL from delta balancing including transaction costs from trading new NDF? Thanks.

## Answer by Ezy (score 1)

https://quant.stackexchange.com/a/43407

Your total pnl is the mark-to-market pnl of your option position and its hedge .

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.