Risky annuities on sovr CDS

recepyakar · July 21st, 2014, 11:28 am

Simply I ask:How can i calculate the risky annuity component in CDS pricing ? Is that simply the sum of discounted survival rates in time ? Does it suppose to converge to 1 finally ?Thx in advance,R

bearish · July 21st, 2014, 10:08 pm

QuoteOriginally posted by: recepyakarSimply I ask:How can i calculate the risky annuity component in CDS pricing ? Is that simply the sum of discounted survival rates in time ? Does it suppose to converge to 1 finally ?Thx in advance,RYes, it is the sum of discounted (risk neutral) survival rates. No, in the simplest flat curves approximation it should converge to [$] \frac {1 }{ r + \lambda} [$].

recepyakar · July 22nd, 2014, 4:52 am

Thanks Bearish,Then what about the old rough approximation below? Is that a junk assumption?Spread / (1 - RR) = PD%

bearish · July 22nd, 2014, 10:24 am

The PD% you refer to is the lambda in my asymptotic formula, which specifically would be the risk neutral hazard rate in the flat credit curve scenario. As assumptions go, it may or may not be junky, but it is certainly very crude. To find the value of the risky annuity you take each scheduled payment and multiply by the product of the risk neutral survival probability and the default free discount factor to its date, and add them up (or integrate, if you make the further simplifying approximation of a continuous annuity stream).

recepyakar · July 22nd, 2014, 1:59 pm

gracias senor..