Chapter 4: Structural models of credit risk. Subordinated debt: example. Parameter estimation. Discretisation. Case study (portfolio consulting case study). Shortcomings and extensions.

Chapter 5: Moody's KMV approach. Introduction. Default probability: main elements, steps. Asset value and volatility: estimation (non-linear system of equations and iterative approaches). Default point and distance to default (DD). Expected default frequency (EDF). Merton vs. Moody's KMV. Case studies 2.2 and 2.1.

Chapter 6: Hitting times. Brownian motion. Running maximum and minimum. First hitting times. Reflection principle. Laws: joint distribution and density of (drifted) Brownian motion and its running maximum/minimum and hitting times.

Chapter 7: First passage time models. Black-Cox model: set-up (firm's asset dynamics and default barrier), default time, probability of survival/default, valuation of defaultable bond.

Chapter 3: Corporate liabilities as contingent claims. Equity and debt valuation: PDE approach and probabilistic approach. Examples 3.1 and 3.2. Hedging of a corporate bond. The Greeks and comparative statics (equity and debt). Case study 4.1. Dividends.

Chapter 4: Structural models of credit risk. Promised yield and credit spread, comparative statics and leverage. Bond's risk: elasticity and volatility. Default time and default probability. Recovery rate upon default and implied conditional expected recovery given default. Subordinated debt: payoffs at maturity, and equity and debt (senior and junior) valuation.

Introduction: contact details, learning objectives, syllabus, timetable and lesson plan, assessment, bibliography, and Moodle.

Chapter 1: Foundations for credit risk modelling. Credit risk, outcomes of a default, terminology and notation (default time, default indicator process, exposure at default, loss given default, recovery rate, default loss, probability of default, expected loss), portfolio loss, credit ratings. Example 1.1, case study 4.1 (questions 1, 5, and 6), and other examples.

Chapter 2: Credit scoring models. Introduction, set up, methodology, type-I and type-II errors, univariate discriminant analysis, multiple discriminant analysis (MDA), Altman Z-score, linear probability model, logit model, and probit model. Example and case study 3.1.

Chapter 3: Corporate liabilities as contingent claims. Structural approach, set up, assumptions, payoffs at maturity.