A moment-matching method to generate arbitrage-free scenarios

We propose a new moment-matching method to build scenario trees that rule out arbitrage opportunities when describing the dynamics of financial assets. The proposed scenario generator is based on the monomial method, a technique to solve systems of algebraic equations. Extensive numerical experiments show the accuracy and efficiency of the proposed moment-matching method when solving financial problems in complete and incomplete markets.

[1]  B. Rustem,et al.  Simulation and optimization approaches to scenario tree generation , 2004 .

[2]  Werner Römisch,et al.  Scenario Reduction Algorithms in Stochastic Programming , 2003, Comput. Optim. Appl..

[3]  Michal Kaut,et al.  A Heuristic for Moment-Matching Scenario Generation , 2003, Comput. Optim. Appl..

[4]  Kjetil H yland.  Generating Scenario Trees for Multistage Decision Problems , 2016 .

[5]  S. Bradley,et al.  A Dynamic Model for Bond Portfolio Management , 1972 .

[6]  Jitka Dupacová,et al.  Scenario reduction in stochastic programming , 2003, Math. Program..

[7]  M. J. Rijckaert,et al.  A condensation method for generalized geometric programming , 1976, Math. Program..

[8]  Michael A. H. Dempster,et al.  EVPI‐based importance sampling solution proceduresfor multistage stochastic linear programmeson parallel MIMD architectures , 1999, Ann. Oper. Res..

[9]  Pieter Klaassen,et al.  Comment on "Generating Scenario Trees for Multistage Decision Problems" , 2002, Manag. Sci..

[10]  Alan J. King,et al.  Duality and martingales: a stochastic programming perspective on contingent claims , 2002, Math. Program..

[11]  Scott A. Burns,et al.  A monomial‐based method for solving systems of non‐linear algebraic equations , 1991 .

[12]  W. N. Street,et al.  Financial Asset-Pricing Theory and Stochastic Programming Models for Asset/ Liability Management: a Synthesis , 1996 .

[13]  R. Rockafellar,et al.  Conditional Value-at-Risk for General Loss Distributions , 2001 .

[14]  Ronald Hochreiter,et al.  Financial scenario generation for stochastic multi-stage decision processes as facility location problems , 2007, Ann. Oper. Res..

[15]  Martin R. Holmer,et al.  A stochastic programming model for money management , 1995 .

[16]  Georg Ch. Pflug,et al.  Scenario tree generation for multiperiod financial optimization by optimal discretization , 2001, Math. Program..

[17]  R. Duffin.  Linearizing Geometric Programs , 1970 .

[18]  Michal Kaut,et al.  Stability analysis of portfolio management with conditional value-at-risk , 2007 .

[19]  S. A. Burns.  THE MONOMIAL METHOD: EXTENSIONS, VARIATIONS, AND PERFORMANCE ISSUES , 1994 .

[20]  Michal Kaut,et al.  Evaluation of scenario-generation methods for stochastic programming , 2007 .

[21]  Ton VorstyJuly.  Dynamic Portfolio Insurance: A Stochastic Programming Approach , 1998 .

[22]  S. A. Burns.  The monomial method and asymptotic properties of algebraic systems , 1994 .

[23]  S. Zenios,et al.  Generating Multi-factor Arbitrage-Free Scenario Trees with Global Optimization , 2014 .

[24]  W. Ziemba,et al.  The Russell-Yasuda Kasai Model: An Asset/Liability Model for a Japanese Insurance Company Using Multistage Stochastic Programming , 1994 .

[25]  J. Dupacová,et al.  Scenario reduction in stochastic programming: An approach using probability metrics , 2000 .

[26]  Jitka Dupacová,et al.  Scenarios for Multistage Stochastic Programs , 2000, Ann. Oper. Res..

[27]  Stavros A. Zenios,et al.  A model for portfolio management with mortgage-backed securities , 1993, Ann. Oper. Res..

[28]  George B. Dantzig,et al.  Multi-stage stochastic linear programs for portfolio optimization , 1993, Ann. Oper. Res..

[29]  G. Dantzig,et al.  Large-Scale Stochastic Linear Programs: Importance Sampling and Benders Decomposition , 1991 .

[30]  Pieter Klaassen,et al.  Discretized Reality and Spurious Profits in Stochastic Programming Models for Asset/Liability Management , 1996 .

[31]  Alex Weissensteiner,et al.  No-arbitrage conditions, scenario trees, and multi-asset financial optimization , 2010, Eur. J. Oper. Res..

[32]  William T. Ziemba,et al.  A Bank Asset and Liability Management Model , 1986, Oper. Res..

[33]  Gerd Infanger,et al.  Monte Carlo (importance) sampling within a benders decomposition algorithm for stochastic linear programs , 1991, Ann. Oper. Res..

[34]  Michael Hanke,et al.  No-arbitrage bounds for financial scenarios , 2014, Eur. J. Oper. Res..

[35]  William T. Ziemba,et al.  The Innovest Austrian Pension Fund Financial Planning Model InnoALM , 2008, Oper. Res..

[36]  Jacek Gondzio,et al.  High-Performance Computing for Asset-Liability Management , 2001, Oper. Res..