Interest Rate Modeling: Post-Crisis Challenges and Approaches

Introduction.-1 Post-crisis fixed-income markets.-1.1 Types of interest rates and market conventions.-1.2 Implications of the crisis.-1.3 The new paradigm: multiple curves at all levels.-1.4 Interest rate derivatives.-2 Short rate models for multiple curves.-2.1 Exponentially affine factor models for the short rate and the Spreads.-2.2 Gaussian, exponential quadratic models.-2.3 Pricing of interest rate derivatives, part A: Pricing of FRAs (linear derivatives).-2.4 Pricing of interest rate derivatives, part B: Pricing of caps (optional derivatives).-2.5 Pricing of interest rate derivatives, part C: Pricing of swaptions (optional derivatives).-2.6 Relationship with models from the literature.-3 Multiple-curve HJM framework.-3.1 Setup and main ideas.-3.2 Absence of arbitrage.-3.3 Volatility structures and the corresponding models.-3.4 Pricing of interest rate derivatives in the HJM framework.-4 LMM multiple-curve extensions.-4.1 Libor market model (LMM) with stochastic basis.-4.2 AffineLIBOR models with multiple curves.-4.3 Cross-currency model analogy.-5 Beyond clean valuation of interest rate derivatives.-5.1 TVA (CVA, DVA, FVA) computations for multiple curve models.-5.2 Direct pricing under collateralization and funding constraints.