Fixed Income Models and Credit Risk | Free CAIA Level II Lesson

You value corporate equity as a call option on the firm's assets: shareholders walk away if assets fall below debt owed and keep the excess otherwise. That single reframing (Merton, 1974) turns default probability into a balance-sheet calculation instead of an exogenous event, and it anchors one of three credit-modeling traditions you need to know. Structural models (Merton, KMV) ask why a firm defaults; reduced-form models (Jarrow-Turnbull) ask how much spread the market demands; empirical models (Altman Z, machine learning) ask who looks like prior defaulters.

Types of models underlying investment strategies. Financial models are simplifications of reality. Every model contains exogenous and endogenous variables. An exogenous variable is determined outside the model and taken as given. An endogenous variable is determined inside the model and takes whatever value the model prescribes. In an endowment cash-management model, donation and investment income inflows are exogenous; the amount invested in new deals is endogenous.

Four methodological distinctions classify investment-strategy models:

Importance of methodology: classifying a strategy by these distinctions helps you organize and compare managers.

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Common mistakes

Confusing risk-neutral PD with actual PD. Merton gives $N (- d_{2})$ under the risk-neutral measure, which is systematically higher than actual (physical) default probability because it embeds risk premium. Trap: a question asks for "expected default frequency" and the test-taker reports $N (- d_{2}) = 8%$ when the actual EDF is closer to 2%.
Using full debt in KMV's default point. KMV uses short-term debt plus a partial amount of long-term debt, not total debt. On a firm with $200M short-term and $400M long-term, the correct default point is $400M, not $600M.
Forgetting to scale equity volatility down to asset volatility. Equity volatility of 35% on a firm with $800M equity and $600M debt is levered; the underlying asset volatility is lower (approximately 20% here), found from $σ_{a sse t s} \approx σ_{e q u i t y} \times (E q u i t y / A sse t s)$ . Using 35% directly in Merton's $d_{2}$ dramatically overstates risk.

Bottom line

Equilibrium models (Vasicek, CIR, first-generation) assume a short-rate process; arbitrage-free models (Ho-Lee, BDT, second-generation) calibrate to the observed curve and are fit to traded bond prices.
Vasicek's discrete expected rate is $E [r_{t + 1}] = r_{t} + κ (μ - r_{t})$ ; BDT sets the level from averaged rolled returns and the up-down spread from caplet implied vol, $r_{u} = r_{d} \cdot e^{2 σ}$ .
Loss chain: EAD = principal + interest, RR = PV of recovery / EAD, LGD = EAD(1−RR), and EL = LGD × PD.
Merton: equity is a call on assets and risky debt $D_{t} = K \cdot e^{- (r + s_{t}) τ}$ ; risk-neutral PD = $N (- d_{2})$ and distance to default DD is approximately $d_{2}$ .

Exam shortcut

On a structural-model question, pin down whether the prompt is asking for distance-to-default, risk-neutral PD, or empirical EDF. They are not the same number, and each maps to a different step in the Merton-KMV chain. On a reduced-form question, always divide CDS spread by $(1 - recovery)$ before exponentiating; forgetting this is the single most common 1-point miss.

The full lesson (about 5,742 words, 38 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

model types
fi models intro
bdt model
credit risk economics
structural model overview
merton model
kmv model
reduced form models
empirical credit models
one period binomial
multi period binomial
tree prices formation
convertible valuation
callable bonds tree
multifactor asset pricing
fama french
empirical mf challenges
factor investing
adaptive markets
efficiently inefficient
trend following
divergence
fundamental directional
behavioral finance
directional factors
digital asset valuation
pca statistical factors
multifactor regression
partial autocorrelations
dynamic risk exposure
changing correlation
multifactor return approaches
performance persistence
rv overview
statistical pairs equities
pairs commodity spreads
pairs rates fx
rv market neutral risks
depreciation tax shields
tax deferral gains
after tax comparisons
transaction based indices
appraisal based indices

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