Financial Applications by Jitka Dupacova, Søren S. Nielsen, Werner Römisch, Nicole Gröwe-Kuska, Hercules Vladimirou

General
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  • The document covers scenario generation for multistage stochastic programming models.
  • Contents: Newsvendor Problem; Scenario Generation for the Newsvendor Problem; Two-Stage, Stochastic Program; Newsvendor as a Two-Stage, Stochastic Program; The “Underlying Process” vs. the “Decision Process”; Multistage Stochastic Programming; The WINVEST Case
  • Abstract: Danish mortgage loans have several features that make them interesting: Short-term revolving adjustable-rate mortgages are available, as well as fixed-rate, 10-, 20- or 30-year annuities that contain embedded options (call and delivery options). The decisions faced by a mortgagor are therefore non-trivial, both in terms of deciding on an initial mortgage, and in terms of managing (rebalancing) it optimally. We propose a two-factor, arbitrage-free interest-rate model, calibrated to observable security prices, and implement on top of it a multi-stage, stochastic optimization program with the purpose of optimally composing and managing a typical mortgage loan. We model accurately both fixed and proportional transaction costs as well as tax effects. Risk attitudes are addressed through utility functions and through worst-case (min-max) optimization. The model is solved in up to 9 stages, having 19,683 scenarios. Numerical results, which were obtained using standard soft- and hardware, indicate that the primary determinant in chosing between adjustable-rate and fixed-rate loans is the short-long interest rate differential (i.e., term structure steepness), but volatility also matters. Refinancing activity is influenced by volatility and, of course, transaction costs.
  • The document contains the WINVEST case, an asset/liability management case.
  • Contents: Fundamentals; Classical Models; The GAMS System; Utility Theory; Modeling using Scenarios; Value at Risk; Stochastic Programming; The WINVEST Case
  • Contents: The Dedication, or Cash-Flow Matching (CFM) Model; The Two-Stage Stochastic Program; Multistage Stochastic Programs; Immunization: Present Value, Duration, Convexity
  • Contents: Data process approximation by scenario trees; Generation of scenario trees; Distances of probability distributions; Scenario reduction; Fast reduction heuristics; Constructing scenario trees from data scenarios; GAMS/SCENRED
  • The document provides information on the usage of GAMS/SCENRED.
  • The document covers a subclass of convex risk measures, the polyhedral risk measures.
  • Contents: What is SP?; Basic Concepts; Common modeling approaches of SP; Need and Value of SP; Overview of solution methods; Sample Applications (emphasis on Finance); Active research domains; Information sources
  • Contents: Problem framework & risk factors; Diversification & Hedging policies; Risk management metrics; Scenario Generation; Optimization Models (Stochastic Programs); Introduction of Derivative Securities in Portfolio; Risk/Return Profiles of Portfolios (static tests); Out-of-sample Performance (Consistency); Backtesting (Ex-post performance)