Hello everyone.I understand digitals are usually not priced theoretically (i.e. using half the B-S formula) but as a replicating call/put spread. Currently I am trying to price European digitals in an FX context. Here bid-ask spreads seen in the market become enormous as soon as maturities exceed one year (I see a spread of more than 50 bps on five year vanilla options on EUR/CHF, for instance).It would make sense to pay ask for the long option in the replicating spread and receive bid for the short option in the spread. However pricing like this leads to meaningless digitals prices given the huge difference between the two vols.What is wrong in my description above and how does the market really price FX digitals? Many thanks!

Marcster , I dont have much experience pricing FX Digitals but with IR we use the same logic (ie constructing Call put spreads ) using an Epsilon spread. Ie for example if I am the Bank XYZ and I am Long a Digitial Cap option paying 1 % if E3M greater than or equal to 4%I would construct this as a Long call at 4% and Short call at 4% + Epsilon adjustment (in basis points) . Every bank has its own Epsilon adjustment whic they use to be on the conservative side of pricing - i.e. Buy the options at a cheaper price and gain the area of epsilon over a period of time when the rates have moved sufficiently. Now one argument you can give me is that HOW DO YOU KNOW THAT RATES WILL MOVE past the 4% + Epsilon spread mark (in bp) . Normally these epsilon spreads are relatively small and intuitively you would know that rates would move suffciently to cover up this strategy. However even if it does not move enough and client wants to put out his / her position before maturity , then you would take up the epsilon spread on the secondayr market when you are making the buyback / unwindHope this throws little light.Anyone wanting to join into this thread explaing things a little further , I would be grateful. My humble knowledge is limited to the above.

Another addition I shouldmake to my comment is that the Long Call and Short call spread should reflect te following payout (in line with my example ) = 1%/ Epsilon spread adjustment * Notional . This will magnify the notional and thus help gain the epsilon area .Cheers

Thanks for the answer Randomness,I am doing the same thing for IR digitals as you describe except that we do not trade digitals by themselves but as part of larger structures such that I have found it to be more plausible to use a balanced replication for the digital i.e. first vanilla at strike - (epsilon/2) and second at strike + (epsilon/2). Indeed there is a Pat Hagan paper linked somewhere on this forum which mentions the different possible decompositions in the context of range accrual pricing if this is of interest to you.What puzzles me is that this no longer works in the FX case. I can replicate vanilla FX prices OK by building smiles out of the quoted Straddle/25RR/25BF vols. However I can then not use these vanilla prices in the way mentioned above to obtain the equivalent digital prices quoted by the market! Given I hit vanilla prices OK, I feel there is nothing wrong either with my calculation or the vols I generate.Clearly, in the IR market, this disparity (note also my spread prices do converge to the theoretical BS/GK price as I let epsilon dwindle to zero) would suggest the existence of an arbitrage opportunity. My guess is that this is not the case in FX precisely due to the size of the bid/ask spread, which is no longer negligible. I suspect I may need to add an adjustment for hedging cost along the lines of http://www.math.ethz.ch/~schmock/ftp/pr ... gitals.pdf but would be glad if someone could confirm or deny this before I go further that road.Thanks again.

Marcster , which one by Pat Hagan - Managing Smile risk ? Also your line - "Clearly, in the IR market, this disparity (note also my spread prices do converge to the theoretical BS/GK price as I let epsilon dwindle to zero) would suggest the existence of an arbitrage opportunity" - does confirm that there is an arbitrage opportunity when it comes to trading these sort of structures in the secondary markets. Lets say for example the epsilon I am assuming is 10 and when its time to bid this back in the secondaries I am going to price my structure again with Epsilon at 1 (Zero is not really possible because some systems are not calibrated to accept Zero epsilons) and the difference in pricing can be taken on as a Trading provision or Provisional P&L as some houses may call it. I have observed in the market that on the secondaries a lot of arbitrage exist on IR CRANs. One way to explain this would be the epsilons and another could be the Credit Arbitrage (through changing ASW levels) . I will go through the PDF article and then see if I understand the technicalities to discuss this issue further with a specific relation to your FX questionThanks.

Marcster whats your direct email add pls ? Had some questions on FX Structuring oriented stuff . would be cool if we could e-discuss outside the forum per se cheers

Hi Randomness, no, not that paper by Pat, instead it is called something like "Range notes". I have not got it to hand right now but if you search this forum you should eventually find the correct thread.It is very unlikely that I will be able to answer any questions on FX structuring but do feel free to send me a private message.All the best