Kybernetika 54 no. 6, 1247-1263, 2018

An asset-liability management stochastic program of a leasing company

Tomáš Rusý and Miloš KopaDOI: 10.14736/kyb-2018-6-1247

Abstract:

We build a multi-stage stochastic program of an asset-liability management problem of a leasing company, analyse model results and present a stress-testing methodology suited for financial applications. At the beginning, the business model of such a company is formulated. We introduce three various risk constraints, namely the chance constraint, the Value-at-Risk constraint and the conditional Value-at-Risk constraint along with the second-order stochastic dominance constraint, which are applied to the model to control risk of the optimal strategy. We also present the structure and the generation process of our scenarios. To capture the evolution of interest rates the Hull-White model is used. Thereafter, results of the model and the effect of the risk constraints on the optimal decisions are thoroughly investigated. In the final part, the performance of the optimal solutions of the problems for unconsidered and unfavourable crisis scenarios is inspected. The methodology of a stress test we used was proposed in such a way that it answers typical questions asked by asset-liability managers.

Keywords:

asset-liability management, multi-stage stochastic programming, stress test

Classification:

90C15, 90B50, 90C31, 91G10

paper.pdf

References:

  1. P. Artzner, F. Delbaen, J M. Eber and D. Heath: Coherent measures of risk. Math. Finance 3 (1999), 203-228.   DOI:10.1111/1467-9965.00068
  2. D. Brigo and F. Mercurio: Interest Rate Models - Theory and Practice with Smile, Inflation and Credit. (Second edition.) Springer Verlag, Berlin 2001.   CrossRef
  3. D. Broeders, A. Chen and B. Koos: An Institutional Evaluation of Pension Funds and Life Insurance Companies. De Nederlandsche Bank, 2009.   CrossRef
  4. D. R. Carino, T. Kent, D. H. Myers, C. Stacy, M. Sylvanus, A. L. Turner, K. Watanabe and W. T. Ziemba: The Russell-Yasuda Kasai model: An asset/liability model for a Japanese insurance company using multistage stochastic programming. Interfaces 24 (1994), 1, 29-49.   DOI:10.1287/inte.24.1.29
  5. R. R. Chen and L. Scott: Maximum likelihood estimation for a multifactor equilibrium model of the term structure of interest rates. J. Fixed Incom. 3 (1003),14-31.   DOI:10.3905/jfi.1993.408090
  6. J. C. Cox, J. E. Ingersoll and S A. Ross: A theory of the term structure of interest rates. Econometrica 53 (1985), 385-407.   DOI:10.2307/1911242
  7. M. A. H. Dempster and A. M. Ireland: MIDAS: An expert debt management advisory system. In: Data, Expert Knowledge and Decisions, Springer 1988, pp. 116-127.   DOI:10.1007/978-3-642-73489-2\_11
  8. D. Dentcheva and A. Ruszczynski: Optimization with stochastic dominance constraints. SIAM J. Optim. 14 (2003), 2, 548-566.   DOI:10.1137/s1052623402420528
  9. C. L. Dert: Asset Liability Management for Pension Funds: A Multistage Chance Constrained Programming Approach. PhD Thesis, Erasmus University, Rotterdam 1995.   CrossRef
  10. J. Dupačová and M. Kopa: Robustness in stochastic programs with risk constraints. Ann. Oper. Res. 200 (2012), 1, 55-74.   DOI:10.1007/s10479-010-0824-9
  11. J. Dupačová and M. Kopa: Robustness of optimal portfolios under risk and stochastic dominance constraints. Europ. J. Oper- Res. 234 (2014), 434-441.   DOI:10.1016/j.ejor.2013.06.018
  12. J. Dupačová: Stability in stochastic programming with recourse. Contaminated distributions. Math. Programm. Study 27 (1986), 133-144.   DOI:10.1007/bfb0121117
  13. J. Dupačová: Stress testing via contamination. In: Coping with Uncertainty: Modeling and Policy Issues (K. Marti, Y. Ermoliev, M. Makowski, and G. Pflug, eds.), Springer, Berlin 2006, pp. 29-46.   DOI:10.1007/3-540-35262-7\_2
  14. J. Dupačová and V. Kozmík: Stress testing for risk-averse stochastic programs. Acta Math. Univ. Comenianae LXXXIV (2015), 2, 205-217.   CrossRef
  15. J. Dupačová and J. Polívka: Asset-liability management for Czech pension funds using stochastic programming. Ann. Oper. Res. 165 (2009), 5-28.   DOI:10.1007/s10479-008-0358-6
  16. A. Geyer and W. T. Ziemba: The {I}nnovest {A}ustrian pension fund financial planning model {I}nno{A}{L}{M}. Oper. Res. 56 (2008), 4, 797-810.   DOI:10.1287/opre.1080.0564
  17. J. Hadar and W. R. Russell: Rules for ordering uncertain prospects. Amer. Econom. Rev. 59 (1969), 25-34.   CrossRef
  18. G. H. Hardy, J. E. Littlewood and G. Polya: Inequalities. Cambridge University Press, Cambridge 1934.   DOI:10.1017/s0025557200027455
  19. K. Hoyland: Asset Liability Management for a Life Insurance Company: A Stochastic Programming Approach. PhD Thesis, Norwegian University of Science and Technology, 1998.   CrossRef
  20. J. Hull and A. White: Pricing interest-rate derivative securities. Rev. Financ. Stud. 3 (1990), 573-592.   DOI:10.1093/rfs/3.4.573
  21. W. K. Klein Haneveld, M. H. Streutker and M. H. van der Vlerk: An ALM model for pension funds using integrated chance constraints. Ann. Oper. Res. 177 (2010), 1, 47-62.   DOI:10.1007/s10479-009-0594-4
  22. M. Kopa, V. Moriggia and S. Vitali: Individual optimal pension allocation under stochastic dominance constraints. Ann. Oper. Res. 260 (2018), 1-2, 255-291.   DOI:10.1007/s10479-016-2387-x
  23. T. Kuosmanen: Efficient diversification according to stochastic dominance criteria. Management Sci. 50 (2004), 10, 1390-1406.   DOI:10.1287/mnsc.1040.0284
  24. M. I. Kusy and W. T. Ziemba: A bank asset and liability management model. Oper. Res. 34 (1986), 356-376.   DOI:10.1287/opre.34.3.356
  25. H. Levy: Stochastic dominance and expected utility: Survey and analysis. Management Sci. 38 (1992), 4, 555-593.   DOI:10.1287/mnsc.38.4.555
  26. J. P. Morgan: Risk Metrics. Technical Document. Fourth Edition. Morgan Guaranty Trust Company, New York 1995.   CrossRef
  27. V. Moriggia, M. Kopa and S. Vitali: Pension fund management with hedging derivatives, stochastic dominance and nodal contamination. Omega - Int. J. Management Sci. 2018.   DOI:10.1016/j.omega.2018.08.011
  28. G. Ch. Pflug: Some remarks on the value-at-risk and the conditional value-at-risk. In: Probabilistic Constrained Optimization: Methodology and Application (S. P. Uryasev, ed.), Kluwer, 1999.   DOI:10.1007/978-1-4757-3150-7\_15
  29. G. Ch. Pflug and A. Pichler: Multistage Stochastic Optimization. Springer Series, New York 2014.   CrossRef
  30. S. R. Pliska and Ye Jinchun: Optimal life insurance purchase and consumption/investment under uncertain lifetime. J. Banking Finance 31 (2007) 5, 1307-1319.   DOI:10.1016/j.jbankfin.2006.10.015
  31. T. Post and M. Kopa: Portfolio choice based on third-degree stochastic dominance. Management Sci. 63 (2017), 10, 3381-3392.   DOI:10.1287/mnsc.2016.2506
  32. T. Post, Y. Fang and M. Kopa: Linear tests for dara stochastic dominance. Management Sci. 61 (2015), 7, 1615-1629.   DOI:10.1287/mnsc.2014.1960
  33. R. T. Rockafellar and S. Uryasev: Optimization of conditional value-at-risk. J. Risk 2 (2000), 21-41.   DOI:10.21314/jor.2000.038
  34. R. T. Rockafellar and S. Uryasev: Conditional value-at-risk for general loss distributions. J. Banking Finance 26 (2002), 7, 1443-1471.   DOI:10.1016/s0378-4266(02)00271-6
  35. L. G. Telser: Safety first and hedging. Rev. Econom. Stud. 23 (1955), 1, 1-16.   DOI:10.2307/2296146
  36. O. Vasicek: An equilibrium characterization of the term structure. J. Financ. Econom. 5 (1977), 177-188.   DOI:10.1016/0304-405x(77)90016-2
  37. S. Vitali, V. Moriggia and M. Kopa: Optimal pension fund composition for an italian private pension plan sponsor. Comput. Management Sci. 14 (2017), 1, 135-160.   DOI:10.1007/s10287-016-0263-4