$($Financial Risk Management$)2)$ Consider the following Credit Default Swap $($CDS$)$ spreads $($in bps$)$:

$(1$ year, $25)(2$ year, $38)(3$ year, $54)(5$ year, $68)(10$ year, $102)$

a$)$ With the information in the table above, and assuming an $80\%$ recovery rate, calculate the term structure of hazard rates.

b$)$ Default probabilities can also be calculated from historical data $($e$.$g$.,$ from data provided by rating agencies$).$ Discuss why these probabilities can be different to the probabilities calculated from credit spreads, and explain in which cases should each set of probabilities be used.