Consider two firms with one-year probabilities of default of $p _ { 1 } = 0.10$ and $p _ { 2 } = 0.05$ , respectively. The correlation of default of these two firms is $\rho = 0.30$ . What is the price of a $100 notional one-year maturity second-to-default basket option on these two firms? (Assume the discount rate is zero.)
A) $2.50
B) $5.50
C) $11.25
D) $17.75

Question

Consider two firms with one-year probabilities of default of  $p _ { 1 } = 0.10$ and $p _ { 2 } = 0.05$ , respectively. The correlation of default of these two firms is $\rho = 0.30$ . What is the price of a $100 notional one-year maturity second-to-default basket option on these two firms? (Assume the discount rate is zero.)
A) $2.50
B) $5.50
C) $11.25
D) $17.75

Quizplus · Accepted Answer

The probability of both firms defaulting is calculated using the formula for joint probability with correlation: $P(\text{both default}) = p_1 \cdot p_2 + \rho \cdot \sqrt{p_1 \cdot (1-p_1) \cdot p_2 \cdot (1-p_2)}$. The probability of the second-to-default event is $P(\text{second-to-default}) = P(\text{firm 1 defaults}) + P(\text{firm 2 defaults}) - 2 \cdot P(\text{both default})$. The price of the option is the notional multiplied by this probability.

Consider Two Firms with One-Year Probabilities of Default Of p1=0.10p _ { 1 } = 0.10p1​=0.10

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