Hi, we are trading FX OTC options and our strategy is very cost sensitive. In order to save costs we combine our vanilla trades into spreads of two options ( for instance we trade as a single trade "buy 10mln 3Months 25 delta call sell 10 mln 6M 25delta put" versus trading each leg individually) 

SpreadBidAsk < BidAskLeg1+ BIdAskLeg2

Does anyone know which formula is used by quoting banks to compute spreadBidAsk as a function of Spreads of individual legs 

SpreadBidAsk = F(BidAskLeg1, BIdAskLeg2)

This relationship is non-linear and depends on difference of maturities of two legs and difference in their delta. The further away options are from each other in maturity and in delta space the less saving on bidask you get. I tried to reverse engineering the  formula from the bank quotes but have limited success. If anyone is able to help it would be very useful. Trading RR could be for instance sometimes cheaper than trading individual legs of the RR. 

Out strategy is very cost sensitive and we would like to put this F(BidAskLeg1, BIdAskLeg2) into our optimizer to rduce costs.

Thanks to anyone who could help.

What makes you think you can model the spreads that banks charge you??

The less risk the bank needs to take on, the less the spread they'll charge, hence b/a spreads on packages (especially if there are offsetting risks in the package) are usually tighter than b/a spreads on individual legs - that's the easy part.

But there are other factors, like the balance sheet cost of risk for the bank, how easily they can recycle the risk, and last but not least, how much spread does the trading desk want, how much the sales desk wants, how they measure counterparty risk etc etc.

 If I may give some general advice to you:
Instead of trying to model how banks quote / determine spreads, keep it simple:
- When you ask for prices, put banks in competition. Ask around 3 banks (depending on the type of option), but don't ask the whole street. That's senseless and just pisses ppl off, and would probably work against you anyway, especially if you trade larger sizes
- Try to trade packages as much as possible
- Monitor the hit ratio of the banks obviously, but also try to find out the axes of the banks, what they're good in etc
- Maintain good relationships with counterparties

Thanks, we do ask a several banks, we trade electronically with.

I think I can model spreads because it looks like all banks discount them similarly, hence I assumed they all used similar model behind the front end (we trading electronically and prices coming back within milliseconds, hence it is unlikely humans manually adjust spreads, there is a model behind pricing, which seems to be consistent between banks)

Looks like they all discount spread similarly. Of course there are variations but seems they are using similar methodology, one thing we noticed is usually spread larger the larger the vega of the traded structure is. The logic is of course if banks buy sell vega from/to us  they need to hedge it in the open market. But we failed to reverse engineer it further. I thought it might be a common knowledge among FX OTC vol traders how spread price is computed. 

Well ok, even if my comments are directed more at exotic strucutres, whereas you trade vanilla options (?), i still don't think there is a general model for spreads. Maybe you can take a look at the papers by Leland to start with, and Zakamouline on factoring in transaction costs, but going beyond those I'd say is firm specific and/or related to market microstrucutre.

Yes, I am trading vanillas only. Thanks I will look at the papers. Agree banks probably have different implementations of spread pricing, but they all likely to capture the same concepts of how cost is calculated, as in real life they tend to agree with each other. Will be happy to adopt any of their model, as it is a bit tricky to reverse engineer. But thanks a lot for the papers maybe they guide me in the right direction. tks

If you have access to historical options flow trades, you can look for some "fit" for the 25D RR.

Is there an equivalent of Trade-Alert for FX options?

Not aware of similar to Trade-Alert system for FX options. Have historical prices of mid RR 25D but not their bid-ask spreads. Thanks for the tip