The ABC Bank enters into a credit default swap with XYZ Financial.The swap runs for 5 years and is based upon a term loan to LMN Corp.The size of the protection payment is 5% per year.Unfortunately,LMN goes bankrupt a year after this swap agreement becomes effective.Even with a 75% recovery value on the underlying loan,XYZ has paid ABC $20 million for settlements.How much has ABC lent to LMN?

Question

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The protection payment is 5% of the amount lent to LMN Corp. Let X be the amount lent to LMN, then the protection payment each year is 0.05X. Over the 5 years, the total protection payment that XYZ pays to ABC is 0.05X * 5 = 0.25X.
When LMN goes bankrupt, XYZ has to pay ABC based on the notional amount of the underlying loan (i.e. the amount lent to LMN). However, XYZ only receives a 75% recovery value on the loan.
So, ABC would receive 100% - 75% = 25% of the notional amount. This payment is calculated to be $20 million, so we can set up the equation 0.25X = $20 million and solve for X:
0.25X = $20 million
X = $80 million
Therefore, ABC lent $80 million to LMN Corp. and the answer is B.

The ABC Bank Enters into a Credit Default Swap with XYZ