Digital Option question

erstwhile · March 4th, 2005, 2:54 pm

i think that's not quite right, as both calls could knock in, and then the market going down would mean the calls are worthless.if you have to use up-in options, use an up-in-call spread long and an up-in-put spread short.then when everything has knocked in, you have a "finance box" (putspread plus callspread)

braiescu · March 4th, 2005, 3:05 pm

Thank you for an immediate response!If i hit the limit, I take my money and do not care about the future.So, is it correct pricing BEFORE it reaches the limit?Alexandru

erstwhile · March 4th, 2005, 3:26 pm

actually i just realised i am wrong!this would give you a "pay-end" digital, which pays out at maturity if you ever hit the barrier during the life.a "pay-now" digital will be different by the NPV of the cash - oops - sorry about that!i actually doubt that you can synthesize the "pay-now" digital using only up-in options.

Jezza · March 5th, 2005, 8:20 pm

two things- Barrier shift (if you digital is at hit),- Time shift (if your options is at maturity,- or both, if the size is large and you can't spread the hedge.

Jezza · March 5th, 2005, 8:22 pm

two things- Barrier shift (if you digital is at hit),- Time shift (if your option is at maturity),- or both, if the size is large and you can't spread the hedge.

xdlyn · June 22nd, 2006, 6:13 am

Hi Exotiq, May I know what is the value for your dK? I found that when set dK = 1bp even the premium of the digitals are not accruate. Any suggestions on this? Thanks, Leann

xdlyn · June 22nd, 2006, 6:13 am

Hi Exotiq, May I know what is the value for your dK? I found that when set dK = 1bp even the premium of the digitals are not accruate. Any suggestions on this? Thanks, Leann

jokeoh · March 5th, 2007, 8:19 pm

Hi Jezza,Regarding your points on time shifts and/or barrier shifts.I don't understand how these smoothen your greeks out.to be honest, in the case of european digitals, callSpeads will do the trick.say, however, we have a 1y downIn @70% atm put on the SPX and that we're selling it.to price this we use a PDE method and local volatility.to book it, are you suggesting we book a 72.5% downIn put?this, however, would suffer from the same issues as the 70% downIn put.

zrj · March 7th, 2007, 9:04 pm

if u are short an american digital, u really do not need that kind of gamma smoothing... for the record, in case u were long, the shifting goes same way as your stop/loss, not opposite