I've come across this equation in a text and can't figure out what part of it is doing.

(Using quarterly installments)

$\frac{1}{4*10^4}s^t \sum\limits_{u=1}^{4t} p_{0.25u}[(1-\pi_{0.25u}) + \frac{1}{2}(\pi_{0.25u-1} - \pi_{0.25u})] = (1-R) \sum\limits_{u=1}^{4t} p_{0.25u}(\pi_{0.25u-1} - \pi_{0.25u})$

Where $p_{0.25u}$ is the price of a risk free zero coupon bond maturing at time $t$.

Why are we dividing the left hand side by $4*10^4$?

  • $\begingroup$ Can you cite the source of the equation please? $\endgroup$ Aug 24 '15 at 1:06
  • $\begingroup$ @KyleBalkissoon it comes from Malz - Financial Risk Management Models, History and Institutions. ps: I corrected a typo in the equation $\endgroup$ Aug 24 '15 at 1:09

The $10^4$ factor is to calculate the answer in bps (basis points). It looks like $4$ is the denominator for the summation of the quarterly installments.

  • $\begingroup$ Oh I didn't catch that re the bps. Making it quarterly is bc the spread is annual them? $\endgroup$ Aug 24 '15 at 16:11
  • $\begingroup$ The CDS spread is bps/year in Malz. $\endgroup$
    – jaamor
    Aug 24 '15 at 17:11
  • $\begingroup$ If it's already in bps/year, why do we need the 10^4 factor? $\endgroup$ Aug 24 '15 at 17:15
  • $\begingroup$ Because 1-R is not in bps. $\endgroup$
    – jaamor
    Aug 24 '15 at 17:18

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