3.1.Hull Ch 22

Bonds above BBB rating are considered investment grade, while lower rated bonds are considered speculative.

• Historical: collect data from firms that start w/ same credit rating
• From bond price: bond price already reflects expected loss from default. Approximate: s = h(1 - R). Exact: PV(loss) = PV(bond @ r_f) - PV(bond @ y)
• Using equity price: unless the 2 previous techniques this one is not subject to infrequently updated ratings. Instead it infers the bond price at any time from firm's stock price, where p(default) = N(-d₂)

• Netting: net any transaction for which money is due against amts that may be owed to that same counterparty
• Collateral requirementes: in form of cash or mktable securities
• Downgrade trigger: certain actions occur upon credit downgrade

• Structural models: correlate stochastic processes
• Reduced form models: assume hazard rates for different companies follow a stochastic process and are correlated w/ macroeconomic variables

Multivariate distribution of 2 or more rdm variables which are both between 0 and 1. It can be used to describe the degree to which 2 or more probabilities are dependent on each other.

• Suppose t_A and t_B are the times to default
• x = N^-1[Q(t)], where Q(t) is the cum p(default)
• Then x is a normally dist rdm var
• The joint probability of A and B defaulting can be generated from a multivariate normal dist by calculating the prob of observing these transformed variables x_A and x_B from a joint standard normal dist w/ a correlation coeff ρ
• One-factor model: x_i = a_i + √(1 - a_i²)Z_i
• Q(T|F) = N[N^-1[Q(t)] - √(ρ)F] / √(1 - ρ)

• Attempts to determine a dollar amt that credit losses will not exceed w/ some high prob.
• Time horizon is usually a year or more.
• Gaussian copula: V(X,T) = N[N^-1[Q(t)] + √(ρ)N^-1(X)]/√(1-ρ)
• Credit metrics model: use credit migration matrix to simulate credit rating changes