FX Option Volatility Quotes and Time-to-Expiry Conventions

# FX Option Vol Quotes (Days or Days+Time to Expiry)


# FX Option Vol Quotes (Days or Days+Time to Expiry)












I understand FX Options are often quoted via ATM, RR, BF for 10/25 deltas. There are many resources that outline how to convert those quotes back into absolute strike space (using spot delta or forward delta, premium adj or unadj, etc). For details, see e.g. A Guide to FX Options Quoting Conventions by Dimitri Reiswich and Uwe Wystup.

For example, the formula for the ATM Delta-Neutral Strike is $$K_{ATM} = f\cdot \exp\left(\frac12\cdot\sigma_{ATM}^2\cdot\tau\right)$$ with $f$ the FX forward, and $\sigma_{ATM}$ the quoted ATM vol, and $\tau$ the time to expiry.

What is confusing me is whether $\tau$ is meant to represent

- Only Full Days to expiry (as is standard in Fixed-Income), or

- Days + Time to expiry (as is standard in normal Option Pricing)

Bloomberg appears to be using 1. To verify this claim, let us consider a 1-day FX Option (as the "time" component would be most prominent). Below is a BBG screenshot showing the same option, but priced 20 hours apart (2am vs 10pm). Curiously, all results are exactly the same:

We can easily replicate $K_{ATM}$ which is `0.99433055` (as per the screenshot). For this, we need to following:

- The Forward, which is `0.9943155 = 0.99425 + 0.655 / 10000 = Spot + Points`.

- The ATM Vol, which is `10.5125% = (9.360% + 11.665%) / 2`.

- The Time to Expiry, which is `0.002739726 = 1 / 365 = 1 day`.

Putting it all together gives `K_ATM = 0.9943155 * exp(0.5 * 0.105125^2 * 0.002739726) ≈ 0.99433055`, which matches the ATM strike given by BBG exactly.

Any `tau != 1 / 365` gives a strike that does not match anymore.

So I wonder, is BBG correct in ignoring time, and only computing $\tau$ as full days to expiry? Is this the "convention" for quoting FX vols? Or should a "correct" model calculate $\tau$ more accurately (i.e. inclusive of hours & minutes)?

## Answer by AKdemy (score 4)

https://quant.stackexchange.com/a/72028

Most appropriate pricing will use the exact time to expiry.

`OVML` is neither a trading tool (FXGO would be at Bloomberg) nor an order management system (`TOMS` for sell-side, `AIM` for buy-side at Bloomberg).

`OVME` (for equity) offers that setting, but by default it is off. `OVML` only has a setting to price the deal at the expiry date. Other than that, it uses only full days to eypiry. I can only guess the exact reason but likely it was a simple cost-benefit decision that was made when this was implemented. Bloomberg offers the aforementioned systems and golden copy intraday snapshots (BVAL) as premium systems.

Just like `MARS` (and `OVML` by default) will price every exotic deal with Vanna Volga, which is very outdated. If you pay extra, you get access to SLV as well as some additional features (depending on numerous add-ons with different price tags for each).

Edit

I think you are somewhat overcomplicating matters here. What you see for FX quotes (on Bloomberg `OVML` and `OVDV`) are only indicative over-the-counter (OTC) quotes, which in turn are by default going through the Bloomberg generic (BGN) algorithm. This is what you see on `OVDV` as well as `OVML`. These quotes have a specific cut-off. So they do imply an expiry time at say NY 10am.

If you now switch to an expiry at say NY 5pm you will get interpolated (hence white) values to account for the difference in time to expiry.

Either way, these quotes are not executable and simply indicative for what the market may quote, if you request a quote (RFQ). Since the cut-off is defined in the quote, market makers who contribute a quote will usually have that in mind. If you want to be certain, you will need to switch to a market maker of your choice and reach out to them, to get a clear answer if they accurately take this into account.

However, if you go back in time, Bloomberg (without additional premium services) will anyhow ONLY show you a single time (5pm NY) because intraday pricing is not available. That is why it does not matter what time you enter on `OVML` (as long as you are before 5pm NY).

My machine is currently set to GMT+2 which means that only after 11pm do I flip past 5pm NY. Therefore, at 11:59pm, it shows 0 days and a different exchange rate, which is the closing price according to BGN of the next day (HP is not showing all decimals, which is why you see 0.9943).

Desktop services at Bloomberg are not designed for intraday pricing (especially not historically). During a given day, you get constant updates, reflecting the current market data.

Turning to equity, if you look at `OVDV` and `OVME`, you also see OTC pricing. The IVOL is computed from listed options but `OVME` (unless you load it with a specific listed option ticker) will also be an OTC pricer. It uses the same logic, meaning you have only access to end of day prices. Even if you set `OVME` to use exact time to expiry, it will only change the $t$ in Black Scholes. Spot, IVOL and everything else is constant. So the only reason the computed price changes is that $t$ changes.

If your trade time goes back prior to the latest update of `OVDV` the day before, it flips to the previous day (even if it means over a weekend!). The reason `OVDV` has only specific set times is that it is quite complex to compute a full vol surface from listed option prices. The values do not match exactly because the tenor is from listed expiry dates and even with standard tenors you cannot go below 1W on BBG. Also, the strike is not ATM (which also ultimately depends on market data).

In any case, if your set time goes past the last available time at the previous day, you flip to the next days end of day surface (22nd of August here) and use that value for the entire day until you go past the time where the last available surface was created. After that, it flips over to the next days end of day value for IVOL.

I think the bottom line is that Bloomberg's desktop applications are not designed for anyone who needs that much detail and accuracy. Nonetheless, Bloomberg's tools are fairly complicated and automate almost everything (from data collection, to surface inter- and extrapolation, to modelling; for FX you can even take events like economic releases into account using `VCAL`) but simplify certain things. On one hand, this is done because Bloomberg offers premium solutions for more detailed pricing and computations, on the other hand many (large) market makers anyhow use their own in house tools. Most price takers find the solutions Bloomberg offers sufficient, more accurate and automated than they could do own their own, or find elsewhere for that price.