International Assets Allocation with Risk Management via Multi-Stage Stochastic Programming

In this paper, we develop a multi-stage stochastic programming model for dynamic international portfolio risk management with options in an integrated view. Upon scenario trees, the model can automatically compute the optimal hedging strategies, which provides rolling and dynamic decisions for how much option positions should be established and how much should be liquidated, while simultaneously allocating the corresponding underlying assets. Extensive numerical analyses strongly verify the effectiveness of the model, especially in market downturns, and support the computational feasibility and performance of the model.

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

[2]  S. Zenios,et al.  Pricing options on scenario trees , 2008 .

[3]  Richard C. Grinold,et al.  Mean-Variance and Scenario-Based Approaches to Portfolio Selection , 1999 .

[4]  R. Ferstl,et al.  Cash management using multi-stage stochastic programming , 2008 .

[5]  Jun Liu,et al.  Dynamic Derivative Strategies , 2002 .

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

[7]  Pei-wang Gao.  Options strategies with the risk adjustment , 2009, Eur. J. Oper. Res..

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

[9]  Auke Plantinga,et al.  The Dutch triangle - A framework to measure upside potential relative to downside risk. , 1999 .

[10]  Fouad Ben Abdelaziz,et al.  Multi-objective stochastic programming for portfolio selection , 2007, Eur. J. Oper. Res..

[11]  A. Neuberger,et al.  How Large are the Benefits from Using Options? , 2002, Journal of Financial and Quantitative Analysis.

[12]  Kourosh Marjani Rasmussen,et al.  Mortgage loan portfolio optimization using multi-stage stochastic programming , 2007 .

[13]  P. Lindberg,et al.  Back-testing the performance of an actively managed option portfolio at the Swedish Stock Market, 1990–1999 , 2003 .

[14]  C. Aliprantis,et al.  Minimum-cost portfolio insurance ☆ , 2000 .

[15]  R. C. Merton,et al.  The Returns and Risk of Alternative Call Option Portfolio Investment Strategies , 1978 .

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

[17]  William T. Ziemba,et al.  Calculating Risk Neutral Probabilities and Optimal Portfolio Policies in a Dynamic Investment Model with Downside Risk Control , 2004, Eur. J. Oper. Res..

[18]  Auke Plantinga,et al.  The Dutch Triangle , 1999 .

[19]  Masao Fukushima,et al.  Portfolio selection under distributional uncertainty: A relative robust CVaR approach , 2010, Eur. J. Oper. Res..

[20]  Matthias Muck.  Trading strategies with partial access to the derivatives market , 2010 .

[21]  H. Henry Cao,et al.  Information, Trade, and Derivative Securities: Table 1 , 1996 .

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

[23]  Mehmet Horasanli.  Hedging strategy for a portfolio of options and stocks with linear programming , 2008, Appl. Math. Comput..

[24]  R. Korn,et al.  Optimal control of option portfolios and applications , 1999 .

[25]  Hercules Vladimirou,et al.  Optimizing international portfolios with options and forwards , 2011 .

[26]  Christos Papahristodoulou.  Option strategies with linear programming , 2004, Eur. J. Oper. Res..

[27]  Nico van der Wijst,et al.  Optimal portfolio selection and dynamic benchmark tracking , 2005, Eur. J. Oper. Res..

[28]  Georg Ch. Pflug.  Optimal scenario tree generation for multiperiod financial planning , 2001 .

[29]  S. Zenios,et al.  CVaR models with selective hedging for international asset allocation , 2002 .

[30]  Jacek Gondzio,et al.  Hedging Options under Transaction Costs and Stochastic Volatility , 2003 .

[31]  J. Harrison,et al.  Martingales and stochastic integrals in the theory of continuous trading , 1981 .

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

[33]  F. Sortino,et al.  DOWNSIDE RISK - CAPTURING WHATS AT STAKE IN INVESTMENT SITUATIONS , 1991 .

[34]  Rudi Zagst,et al.  Integrated portfolio management with options , 2008, Eur. J. Oper. Res..

[35]  Sheridan Titman,et al.  Performance Measurement without Benchmarks: An Examination of Mutual Fund Returns , 1993 .

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

[37]  M. Brennan,et al.  Information, Trade, and Derivative Securities , 1997 .

[38]  Alex Weissensteiner,et al.  Asset-Liability Management Under Time-Varying Investment Opportunities , 2009 .

[39]  Stein W. Wallace,et al.  Generating Scenario Trees for Multistage Decision Problems , 2001, Manag. Sci..

[40]  Pankaj Sinha,et al.  HEDGING GREEKS FOR A PORTFOLIO OF OPTIONS USING LINEAR AND QUADRATIC PROGRAMMING , 2010 .

[41]  M. Fukushima,et al.  Portfolio selection with uncertain exit time: A robust CVaR approach , 2008 .

[42]  Alex Weissensteiner,et al.  Scenario tree generation and multi-asset financial optimization problems , 2013, Oper. Res. Lett..

[43]  Hercules Vladimirou,et al.  A dynamic stochastic programming model for international portfolio management , 2008, Eur. J. Oper. Res..

[44]  D. Sondermann.  Hedging of non-redundant contingent claims , 1985 .

[45]  Martin B. Haugh,et al.  Asset allocation and derivatives , 2001 .