Problem $2\mathrm{.}4$: Bootstrapping the hazard rates from CDS spreads Consider a Credit Default Swap with maturity $2$ years, paying a premium with semi$-$annual frequency.

Assume that defaults can occur only at times $0\mathrm{.}25$ years, $0\mathrm{.}75$ years, $1\mathrm{.}25$ years and $1\mathrm{.}75$ years, as in the example discussed in class. $($This is similar to the simplifying assumption made in the example discussed in Chapter $25\mathrm{.}2$ in Hull; in real applications the defaults are allowed to take place any day, but this would complicate the computation.$)$

The CDS spread is $175$ basis points. Assume that the risk$-$free interest rate is $5\mathrm{.}0\%($with continuous compounding$)$ and the recovery rate is $R=40\%.$

What is the hazard rate of the reference name? Assume a constant hazard rate for the entire maturity of the CDS$.$