Financial Risk Manager Part 1

Financial Risk Manager Part 1

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A fixed-income analyst is examining the annual default rate within a bond portfolio and has determined that it follows a Poisson process. Historical data suggests that, on average, there are four bond defaults per year. Considering that these defaults occur independently of one another, calculate the probability that there will be at most one default in the next year.

Explanation:

C is correct. Using the Poisson distribution approach, and assuming the average number of defaults is AA per year, the probability of nn defaults over a period (year) tt is given as: P(K=n)=e−λλnn!P(K = n) = \frac{e^{-\lambda} \lambda^n}{n!} Therefore, P(at most one default)=P(one default)+P(no default)P(\text{at most one default}) = P(\text{one default}) + P(\text{no default}) P(at most one default)=(4×11!)e−4+(4×10!)e−4=0.0733+0.0183=9.16%P(\text{at most one default}) = \left( \frac{4 \times 1}{1!} \right) e^{-4} + \left( \frac{4 \times 1}{0!} \right) e^{-4} = 0.0733 + 0.0183 = 9.16\%

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