I am pricing options on CDS whereT = expiration date of option, start of CDSV = option valueV* = option value conditional on no default by TP(T) = Prob(no default by T)I am using the Hull-White extension of Jamshidians interest rate swaption extension of Black's model.We haveV = P(T).V* is the black box model output.a) A quote I got is for an option on a single-name CDS with "no-knockout". I don't understand how this works practically in the case of default before T, but it seems I should price it as V* = V/P(T). Am I missing something?b) I also need to price a CDS on the index, say CDX.NA.IG. As a first glance at pricing, I look treat it like a single name, with the index spread as default probability input. The big difference is that the index will be around in 6 months, a.s., although possibly with some different underlying names. But using the spread curve, P(T)>0. So again I price it as V*.c) My black box outputs greeks, which I take as, say, Vega* = Vega/P(T). For theta, theta* ~= theta/P. Better, assume a form for P(T) and Theta* = Theta/P - V/P(T)*d(log(P(T))/dt evaluated at t = 0, T-t = T, right?d) Is there a more sophisticated way to price options on CDS indices that stays close to the HW/J/B model?

Maybe the better approach is to proceed as in Hull-White, conditioning on no default to T, but now the piece in states of the world with a default are not zero. Break up default into 1(default) = 1(bankruptcy)+1(restructuring)+1(failure to pay) and then price the option given no knock out in each state. For example, in states of the world {bankruptcy} there option is still worth zero (still knocks out). So the only possible added value is where there could be a second credit event after option expiry to collect on (failure to pay and the company is still around to have another failure to pay or bankruptcy).Also, can anyone shed any light on the practical mechanics of no-knock CDSwaptions?

Most single name CDS swaptions knock out on default. ISDA has recently released a draft confirmation template. So why do you bother looking at the case without knockout?BTW: Hull & White didn't come up with the extension of the Black model to the defaultable case. It was first published by Schönbucher in a 1999 working paper.

Thanks for your reply. According to some of the market makers our traders deal with, some banks are now quoting "no-knockout" options on CDS. Of course, it seems natural for it to knockout, and that feature is built into the pricing method. Hence, my questions.Even if it is irrelevant for single names, my question still stands for pricing options on CDS Indices. Any clarification is appreciated.

for receivers: No-knockout = knockout for payers: No-knockout = knockout + cost of protection from t=0 to expiry

You can add to it the separation betwenn Acceleration or no Acceleration.In the first case, the holder of the payer option use his right to buy protection just after the default of the underlying, however in the 2nd case he waits until the Maturity to use it.

Thanks HTFB. Makes sense. Can you address the issue of pricing CDS Options on indices -- ie., index spread implies some prob of default which is used to discount in Hull-White model; but the index should be will be around (almost) almost surely in 6mo?I guess the mechanics for a regular no-knock is that for a payer, in case of default before option maturity, the user can immediately exercise the option?

Index Payers: It's no-knockout with respect to each of the names...not the whole index! Each name in the index is physically settled on credit event. So if 1 of the names is about to default, you can exercise the payer into an Index swap and then benefit from the name that defaults. if you exercise early:You receive notional/N * (1-R) .... where N = # of names in index and R = recoveryYou give up remaining optionality (usually not a big deal)If strike is OTM then you still shouldn't exercise...although it would be pretty hard for it to still be OTM once a name is about to default.

thanks again. I guess my question is whether I can price the option on the index without pricing each of the underlying names individually. Suppose I don't even know the underlying names and I just want to use the market spread curve for the index and use my black box to price the option and get sensitivies...Also, how is a no-knock option different from an american?

"whether I can price the option on the index without pricing each of the underlying names individually. " absolutely ... the option exercises into the Index Swap, not swaps on the component names. Since these are different (upfronts, fixed coupons, basis b/w NAV of names and index, etc.) you should use only the index curve. It's also a lot easier...you don't need correlations."how is a no-knock option different from an american? " It's not

Once you know/assume the processes for all the underlyings of the index and their dependency structure, the no-arbitrage index distribution is determined. Thus, assuming that the index is, lognormally (replace with any distribution you like) distributed, may be inconsistent with the assumptions for the underlyings.However, given the higher price transparency for an index and the (current) nonzero basis, it appear logical, at this stage, to model the index on its own and live with the potential inconsistency.

HTFB, u suggested for receivers: No-knockout = knockout for payers: No-knockout = knockout + cost of protection from t=0 to expiry I have made a model that does exactly the same. However, won't the put-call parity cease to hold if we add a front-end protection to payer and leave the receiver as it is given by the Black model...?

Btw, I am talking about a single name CDS option without knock-out

HTFB,with reference to your post about pricing index options, are you suggesting that we price a single-name option without knock-out exactly the same way we do an index option; since u suggest that we just use the index spread for all the index constituents...