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I'm tying to reconcile the delta value for an FX option. I'm comparing the results to Bloomberg to verify our calculation is correct.

I've looked at this - Quantlib: Greeks of FX option in Python but it doesn't show where Rd (domestic interest rate) Rf (foreign interest rate) came from.

The option I'm trying to calculate the Delta for is as follows:

enter image description here

The Black-Scholes formula for delta is as follows:

enter image description here

where:

enter image description here

Using the information for the ScreenShot I get:

S = 108.947

X = 83.200

T = 83 / 365 = 0.2274 years

σ = 15.703% = 15.703 / 100 = 0.15703

Where can I find the Rd (domestic interest rate) Rf (foreign interest rate) from the screen shot? Do I need to access this from another screen in Bloomberg?

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    $\begingroup$ Do CAD Depo and JPY Depo look like intetest rates? $\endgroup$ Aug 10, 2023 at 16:11
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    $\begingroup$ Does this answer your question? Quantlib: day-by-day evaluation of option value $\endgroup$
    – AKdemy
    Aug 10, 2023 at 17:21
  • $\begingroup$ I know you referenced that question but it has the inputs highlighted and a complete replication of the result in Julia and quantlib. $\endgroup$
    – AKdemy
    Aug 10, 2023 at 17:25
  • $\begingroup$ @Akdemy I see the rates as CAD Depo (4.754%) and JPY Depo (-0.361%). Thanks for pointing this out. Will test these inuts $\endgroup$ Aug 10, 2023 at 18:29
  • $\begingroup$ Actually, you do realize you compute a digital here? That is a spread and you cannot replicate that easily because you do not have access to the vols used. $\endgroup$
    – AKdemy
    Aug 10, 2023 at 19:41

1 Answer 1

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What you look at here is not a normal option. The type is called DIVA, which stands for digital vanilla, which is a binary option.

Bloomberg computes this via a tight spread. However, you have a few difficulties here:

  • The spread will use two different IVs, which is not displayed on the GUI. You would need to get this by applying the spread (1% of strike in BBG's case) and reading of the IV of each individual option.
  • Notional is usually in ccy2 in a digital: JPY in your case
  • Since your notional is in ccy1 you actually no longer have a cash or nothing, but an asset or nothing binary option. The final exchange rate will matter for your actual payoff in this case, which is why you need to scale it by a vanilla call option.
  • Delta (by the way, d1 is not delta anyways, also not in the vanilla case) will work very differently here. It will be the sum of both vanilla option hedge values.

In all honesty, I'd just trust Bloomberg here.

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