Abstract
Portfolio replication is a powerful tool that has proven in practice its applicability toenterprise‐wide risk problems such as static hedging in complete and incomplete marketsand markets that gap; strategic asset and capital allocation; benchmark tracking; design ofsynthetic products; and portfolio compression. In this paper, we revise the basic principlesbehind this methodology, currently used by financial institutions worldwide, and presentseveral practical examples of its application. We further show how inverse problems infinance can be naturally formulated in this framework. In contrast to mean‐variance optimization,the scenario approach allows for general non-normal, discrete and subjectivedistributions, as well as for the accurate modeling of the full range of nonlinear instruments,such as options. It also provides an intuitive, operational framework for explaining basicfinancial theory.
Similar content being viewed by others
References
P. Carr and A. Chou, Braking barriers, Risk 10(9)(1997)139–146.
D.R. Carino and W.T. Ziemba, Formulation of the Russell-Yasuda Kasai financial planning model, Operations Research 46(4)(1998).
R. Dembo, Scenario optimization, Annals of Operations Research 30(1991)63–80.
R. Dembo, Optimal portfolio replication, Algorithmics Technical Paper series 95–01.
R. Dembo, D. Rosen and D. Saunders, Illiquid neutrality: On implied risk neutral probabilities with transaction costs and liquidity constraints, Algorithmics Working Paper, 1997.
R. Dembo, L. Merkoulovitch and D. Rosen, Images of a portfolio, Algorithmics Technical Paper series 97–02, 1997.
E. Derman, D. Ergener and I. Kani, Static option replication, Goldman Sachs Quantitative Strategies Research Notes, May 1994.
E. Derman and C.N. Kani, Implied trinomial trees of the volatility smile, The Journal of Derivatives (Summer 1996).
D. Duffie, Dynamic Asset Pricing Theory, Princeton University Press, Princeton, 1992.
S.P. Huestis, The use of linear programming in the construction of extremal solutions to linear inverse problems, Classroom Notes, SIAM Review 38 (1996)496–506.
F. Jamshidian and Y. Zhu, Scenario simulation: Theory and methodology, Finance and Stochastics 1(1997)43–67.
C. Joy, K.S. Tan and P.P. Boyle, Quasi-Monte Carlo methods in numerical finance, Management Science 42(1996)926–938.
H. Konno and H. Yamazaki, Mean absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management Science 37(1991)519–531.
R. Litterman, Hot spots and hedges, The Journal of Portfolio Management, Special Issue (1996).
A. MacKay and E.Z. Pressman, Estimating valuator operators in incomplete markets with noises, Working Paper, University of York, 1996.
H.M. Markowitz, Portfolio selection, Journal of Finance 7(1952)77–91.
RiskMetrics™, Technical Document, J.P. Morgan Guaranty Trust Company, New York, 3rd edition, 1995.
M. Rubinstein, Implied binomial trees, Journal of Finance 69(3)(1994).
S.A. Zenios and P. Kang, Mean-absolute deviation portfolio optimization for mortgage-backed securities, Annals of Operations Research 45(1993)443–450.
W.T. Ziemba and J.M. Mulvey (eds.), Worldwide Asset and Liability Modeling, Cambridge University Press, 1998.
Rights and permissions
About this article
Cite this article
Dembo, R., Rosen, D. The practice of portfolio replication. A practical overview of forward and inverse problems. Annals of Operations Research 85, 267–284 (1999). https://doi.org/10.1023/A:1018977929028
Issue Date:
DOI: https://doi.org/10.1023/A:1018977929028