Hi Guys! I wanna compute the intrinsic value of the iTraxx Crossover. I have the time series of the spread of the iTraxx Crossover and the time series of the spread of the single names. How could I compute the upfront payments for each single names? I know I should have the time series of the risky annuity or the time series of the hazard rate curve, but unfortunately they are not available on bloomberg; in bloomberg there is the actual risky annuity but not the historical one. How can I do? The followings are the data I have:- Time Series iTraxx Crossover- Time Series Single names of the index- Implied default probability of the single names (not the default probability for each year, but just the default probability for the entire maturity of the CDS single names)- Time Series of Libor and Swap rate.Thanks in advance.M.C

This is not an exact science, but a reasonable starting point would be to compute risky annuities for each name/date assuming a flat CDS curve along with the relevant swap curve. If you wanted to be more clever you could play around with some generic non-flat curve shapes, but I doubt that the effect would be all that big.

OK..but How can I compute the risky annuity with the few data I have? What is the formula of risky annuity?

Umm - well, this actually takes some work. Only in the special case of a flat discount curve along with a flat credit curve do you get a "formula". Otherwise, you need to do a little numerical integration. This should be in the student forum, but seeing as you have already posted your question in two separate forums (against guidelines), maybe we'll stay here for now. Do you have a textbook that covers credit derivatives?

Yes. But it doesn't mean the term risky annuity. I am looking to compute the time series of risky annuity using a flat hazard rate curve. Could you tell me the formula for risky annuity bearish? Thanks!

QuoteOriginally posted by: Mattew46Yes. But it doesn't mean the term risky annuity. I am looking to compute the time series of risky annuity using a flat hazard rate curve. Could you tell me the formula for risky annuity bearish? Thanks!The expression you want to evaluate is [$]A=\int\limits_0^T P_{0,t} e^{-\lambda t} dt[$], where [$]\lambda[$] is the constant hazard rate and the function [$]P_{0,t}[$] gives you the discount factor to each date [$]t[$]. Of course, if you take the discount factor to be of the form [$]e^{-r t}[$] the integral can be trivially solved analytically, but otherwise you need to use a quadrature.

Hi bearish! I wanna to ask u a confirmation about this formula in order to compute the risky annuity with flat hazard rate: A=e^(-rt)*e^(-λt), where the first term is the discount factor. Right?Thanks!

QuoteOriginally posted by: Mattew46Hi bearish! I wanna to ask u a confirmation about this formula in order to compute the risky annuity with flat hazard rate: A=e^(-rt)*e^(-λt), where the first term is the discount factor. Right?Thanks!At the risk of sounding rude and condescending, questions about how to integrate exponentials belong in the (high school) student forum. And the answer is "no".

you are right bearish. But in the integral which interest rate should I use? Because I have a term structure of interest rate (libor and swap rate). I have to use just one interest rate right? Thank u bearish!

QuoteOriginally posted by: Mattew46you are right bearish. But in the integral which interest rate should I use? Because I have a term structure of interest rate (libor and swap rate). I have to use just one interest rate right? Thank u bearish!I don't think there is an obvious exactly right answer, but a very convenient choice that is not going to be terribly wrong is to simply use the swap rate that most closely matches the index maturity.