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I am just writing my thesis about FX instrument and hedging and one question popped up which I can't solve. Maybe it is silly but cant find anything about it how the delta of a fx spot is defined and I want to hedge it with an option in USD Deltas. The delta of an option is easy just the first derivative of the Garman-Kohlhagen option pricing formula.

I have a GBP/USD FX-SPot trade with T+2 settlement period and the deal is made today on the 8/13/2019. The spot date would be 8/15/2019 (physical exchange). I have the folling parameters:

$$\Delta_{USD_{T+2}} \approx Notional_{GBP} * pips $$

The question is how can I discount the delta to be the value of today.

How would I now discount the delta to today in terms of T+2 to T?

I would use the instantaneous fx spot rate: $$FX_{instantaneous_{GBP/USD}} = FX_{Spot}-(ON+TN)$$ but how can I use it in the approximation above?

If I would look into a USD/CHF FX-Spot trade the delta would look like:

$$\Delta_{USD_{T}} \approx Notional_{USD} * pips = \Delta_{CHF}/FX_{instantaneous_{USD/CHF}}$$

So my two questions:

  1. How can I discount the USD $$\Delta$$ for GBP/USD FX-Spot?
  2. Does the approximation makes sense for USD/CHF?

If not what approach should I use?

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  • $\begingroup$ I think you may be overcomplicating things. The Garman Kohlagen delta is with respect to Spot, and the delta of Spot with respect to Spot is just one. $\endgroup$ – Alex C Aug 16 at 17:36
  • $\begingroup$ Also, "hedging" spot with options doesn't make sense. $\endgroup$ – will Aug 16 at 18:08
  • $\begingroup$ @AlexC, Not in the tardes view. Because 1 is not the proper delta. Here the pips ar eimportant or the curves. $\endgroup$ – NewNY1990 Aug 17 at 7:28
  • $\begingroup$ @will: Why? If I have FX-Spot expiring in two days on a physical delivery of an FX-Spot I should hedge it an Option right? $\endgroup$ – NewNY1990 Aug 17 at 9:31

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