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At 11:52, Tim Bennett says:

Well let's have a look at 11:52 some prices. Currently the cost of 11:57 insuring Greek debt is in excess of 12:02 $\color{green}{2,000}$ basis points. Another way of 12:07 looking at that is that you are paying as a 12:09 premium annually $1/5$th of the value 12:12 of the debt in question. So another way 12:16 of looking at that is: the market is 12:19 effectively giving the chance of Greeks 12:20 going bust within five years over $\color{red}{80\%}$ probability.

Doesn't the cost a Credit Default Swap (CDS) for Greek debt is $\color{green}{20\% (= 2000}$ bp), entail that the chance of default by Greece is also 20%? Why $\color{red}{80\%}$?

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    $\begingroup$ Your "$1-x$" interpretation may not be what this person had in mind. $\endgroup$
    – user18
    Apr 10 '20 at 3:53
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Note that the 20% annual premium would imply a 20% annual default probability. Tim Bennett is then talking about the probability of default within five years.

He might have thought that $$ 1 - Prob(\text{no default for five years running}) = 1 - (1 - 0.2)^5 > 0.8 $$ but this is not true as $$ 1 - (1 - 0.2)^5 \approx 0.67 $$

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If x is a Bernoulli trial with probability $p$ then we can use the binomial distribution to calculate, as @Giskard does, the probability that something doesn't happen in n trials (here five) as $1-(1-p)^5$. And, as he or she points out, this implies a probability of about 67% if p=.2.

However, this neglects recovery rates. Think of the price of a CDS per year as (roughly) equally the expected losses per year. In a competitive, relatively efficient market, and with low transaction costs, you pay for insurance what you expect to lose over the same time period. What are the expected losses?

$$E[L] = p_{default} \cdot E[Loss|default]$$

You can see that if the $E[Loss|default] = LGD = 1$, then the price of the CDS is the expected loss and also the probability of default. If so, then the remainder of the argument is as @Giskard makes it. However, if the $LGD<1$ is lower then this implies the the probability of default is higher at a given expected loss. For example, at a 55% recovery rate (at a standard assumed LGD for sovereigns of 45%) and expected loss of 20% per year, the probability of default per year is 44.4%. An annual probability of default of 44.4% implies a 5 year default rate of 94.7%.

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