Interpreting the Quarterly CDS Spread Equation

Summary

The document explains the scaling on the premium side of a quarterly-pay credit default swap pricing equation. The factor of 10,000 converts a spread expressed in basis points into decimal rate units. The factor of four corresponds to quarterly installments, scaling the annualized spread by one quarter for each payment period.

The equation balances discounted premium payments, adjusted for default timing, against discounted protection payments based on loss given default. The explanation is brief and answers only the unit and payment-frequency question. It does not derive the full pricing relationship, define all variables, or discuss assumptions such as recovery modeling, discount curves, or accrued premium conventions.

Key ideas

• The factor of 10,000 converts a spread quoted in basis points to decimal units.
• The factor of four reflects quarterly premium installments.
• The equation equates the premium leg with the protection leg under its stated assumptions.

Tags

# Explain equation to calculate CDS spread


# Explain equation to calculate CDS spread












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 $4*10^4$?

## Answer by jaamor (score 1, accepted)

https://quant.stackexchange.com/a/19439

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.

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