Theory of Credit Risk Models

Identify sources of credit risk across secured and unsecured loans, public debt, and counterparty exposures, including collateral, credit spreads, and OTC versus exchange-traded derivatives.

Survey credit risk models from qualitative face-to-face and credit score methods to quantitative approaches like the Merton model and Euroland Turnbull with multiple states.

Explore futures and forwards, exchange-traded and over-the-counter derivatives that lock in future prices for underlying assets. Learn long and short payoffs, no-arbitrage pricing, and time-value adjustment for fair strike prices.

Discuss the drawbacks of the Merton model: assumes observable assets, equity as a long call on assets, debt as a zero-coupon short put, and a frictionless market with risk-free rate.

The KMV model extends the merchant model by using distance to default to estimate the one-year probability of default from asset value, debt thresholds, volatility, and Black-Scholes relations.

Compare the kmv model to the merton model, noting kmv supports coupon paying debt and share-derived value. See how market sentiment and equity data inform credit risk.

Examine the euro Turnbull credit migration model and its drawbacks, including time-homogeneity, data limits, state granularity, and credibility concerns of credit ratings.

Explore the random walk model x_t = x_{t-1} + ε_t, where ε_t is white noise, often normal, noting its non-stationarity, growing variance, and independent increments.

The lecture introduces the Markov chain, a discrete-time stochastic process with a discrete state space and the Markov property, using a healthy–ill–dead example to model disease transitions.

Explore stationary probability distributions in finite Markov chains, compute the stationary vector pi, and analyze long-run state distributions and convergence via transition matrices.

Explain T Q X as the chance a life at age X dies before reaching X plus T, and T P X as chance it survives to X plus T.

Explore Kolmogorov's forward differential equation for Markov jump processes by outlining three key assumptions: the Markov property, small-h transition rates, and age-specific constant mortality for t<1 year.

Explore the mathematics of Kolmogorov's forward differential equation for credit risk models, deriving survival dynamics from transition probabilities and the force of mortality.