Consider Two Firms with One-Year Probabilities of Default Of $p _ { 1 } = 0.10$

question 6

Multiple Choice

Consider two firms with one-year probabilities of default of $p _ { 1 } = 0.10$ and $p _ { 2 } = 0.05$ , respectively. The conditional probability of default in one year is $\operatorname { Pr } \left[ D _ { 1 } \mid D _ { 2 } \right] = 0.7$ . What is the probability of a second-to-default basket option that pays $100 if any both firms default within a year? (Assume zero discount rates.)

• A) $0.50
• B) $1.50
• C) $2.50
• D) $3.50

---

Definitions:

Perpetuity

An annuity in which the periodic payments begin on a fixed date and continue indefinitely.

Long-Term Bonds

Debt securities with a maturity of more than 10 years, offering periodic interest payments.

Interest Rates

The cost of borrowing money, expressed as a percentage of the amount loaned, payable to the lender at a specified rate over a given period.

Borrowing Directly

The process where individuals or entities obtain funding directly from lenders without intermediaries, typically through issuing bonds or obtaining loans.