FTD basket / Default time / Survival probability

EMBI · May 28th, 2014, 7:46 am

Hi all!Simple question, I believe, but need some fresh view.I need to price FTD/Nth-TD basket in Excel. No other software is suitable for this particular task unfortunately.There is matrix of time to defaults:Simulation 1: Tau_1_1 - Tau_1_2 - ... - Tau_1_NSimulation 2: Tau_2_1 - Tau_2_2 - ... - Tau_2_N...Simulation M: Tau_M_1 - Tau_M_2 - ... - Tau_M_Nwhere Tau_i_j is time to default of issuer j on simulation i.How can I get survival probabilities from this matrix?

APlus · May 30th, 2014, 8:30 am

You have a basket of default swaps with a lot of n'th to default. There are normally about 2, but not N.>>2.When you have the first default in the first scenario you'l have Tau_1_1, and you'll have Tau_1,2 for the second -to- default. The time between t_j_i = Tau_j_i and Tau_j_(i+1) is the time of survival. With its values, from all the scanarios, you build a histogram, which should look like an exponential. And you fit the Exp(-lambda) on the histogram of t_j_I's. (Ex: I=1 for the first default).