Calculating the Delta of FX option

Question

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:

The Black-Scholes formula for delta is as follows:

where:

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?

Does this answer your question? Quantlib: day-by-day evaluation of option value — AKdemy, Aug 10 '23 at 17:21
I know you referenced that question but it has the inputs highlighted and a complete replication of the result in Julia and quantlib. — AKdemy, Aug 10 '23 at 17:25
@Akdemy I see the rates as CAD Depo (4.754%) and JPY Depo (-0.361%). Thanks for pointing this out. Will test these inuts — Nikesh P4tel, Aug 10 '23 at 18:29
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. — AKdemy, Aug 10 '23 at 19:41
Well, that is not a vanilla FX option - you loaded a stored deal (the Bop*** number shows that) and the option is actually a digital (binary) option. You can see details here. — AKdemy, Aug 10 '23 at 19:51

score 2 · Answer 1 · answered Aug 10 '23 at 20:44

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.

Calculating the Delta of FX option

1 Answers1