Fixed Income Models and Credit Risk

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-score) ask who looks like prior defaulters. Each tradition suits different problems.

Types of models underlying investment strategies. Financial models are simplifications of reality. Every model contains exogenous and endogenous variables. An exogenous variable is an input set outside the model, so you take it as given. An endogenous variable is an output calculated by the model. 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:

Common mistakes

• Confusing risk-neutral PD with actual PD. Merton gives $N(-d_2)$ under the risk-neutral measure. It is a Q-measure, the PD implied by prices if investors were risk neutral, not the true default probability. Trap: a question asks for empirical "expected default frequency" and the test-taker reports $N(-d_2)$.
• Mixing dollar LGD with the loss fraction. LGD is a dollar amount, $EAD \times (1 - RR)$. Multiply PD by dollar LGD to get dollars, or multiply PD by $1 - RR$ to get loss per $1 of exposure. Trap: writing $EL = EAD \times PD \times LGD$ counts exposure twice.
• Using full debt in KMV's default point. KMV uses short-term debt plus a partial amount of long-term debt, not total debt, and the curriculum does not fix that weight. With $200M short-term and $400M long-term debt and an assumed 50% weight, the trigger is $400M, not $600M.

Bottom line

• Classify models as normative/positive, theoretical/empirical, applied/abstract, and cross-sectional/time-series; judge them mainly by predictive ability; P-measures are actual probabilities, Q-measures risk-neutral quasi-probabilities for valuation.
• Loss chain: EAD = principal + interest, RR = PV of recovery / EAD, LGD = EAD(1−RR) in dollars, and EL = EAD × PD × (1−RR).
• Adverse selection is pre-trade (lemons; mitigated by credit history, collateral, loan limits) and moral hazard is post-trade (mitigated by monitoring, restrictions, loan limits).
• Merton (face value K): equity is a call on assets or $V + P - Ke^{-rT}$; debt is a covered call paying $\min(V(T), K)$; $P = Ke^{-rT}N(-d_2) - VN(-d_1)$, $B = Ke^{-rT} - P$, $s = \ln(K/B)/T - r$, and risk-neutral PD = $N(-d_2)$.

Exam shortcut

On a structural-model question, pin down whether the prompt is asking for Merton's $d_2$, KMV's 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 that gives you a spread and a recovery rate, use $s \approx \lambda(1 - RR)$: divide the spread by $(1 - RR)$ to get the intensity before exponentiating.

The full lesson (about 6,685 words, 45 min read) adds 2 worked examples, all 5 common mistakes, a self-check, free in the app.

Learning objectives

• model types
• credit risk economics
• structural model overview
• merton model
• kmv model
• reduced form models
• empirical credit models
• multifactor asset pricing
• fama french
• empirical mf challenges
• asset strategy complexity
• 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
• 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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