6- Credit risk pricing

Question 1

What is the formula for probability of default before t (Q(t))?

Answer 1

Q(t) = 1 - S(t) = 1 - e⁻ˢᵗ

Question 2

What is the variable S(t)?

Answer 2

The probability of the issuer surviving to period t

Question 3

Briefly explain the Recovery rate (R)?

Answer 3

When an issuer defaults, investors can try to recover part of their money (either with reduced coupons, or lower final payment, or extended maturity)

Question 4

Why do credit spreads tend to be slightly lower than hazard rates?

Answer 4

Because positive Recovery rates mean default payoff is also positive

Question 5

What is the probability of default (Q(t)) with a positive recovery rate (R)?

Answer 5

Q(t) = (1 - e⁻ˢᵗ)/(1 - R)

Question 6

What is the main drawback of using bond prices to estimate default probabilities?

Answer 6

Default rates estimated from bonds prices are higher than historical default rates

Question 7

Why do default rates estimated from bond prices tend to be higher than historical default rates?

Answer 7

-Liquidity premium for corporate bonds causing a higher spread
-High correlation of defaults in times of market stress make a higher premium necessary

Question 8

What is the distance to default?

Answer 8

Measures how many standard deviations the asset value can move before triggering a default

Question 9

How do the Black-Scholes distributions change in Credit Risk pricing?

Answer 9

S₀ → V₀
K → D

Question 10

How do you approximate Equity value (E₀) for a spread calculation when the company doesn’t have shares?

Answer 10

Use the Merton model equation