Abstract
Considering the stochastic exchange rate, a four-factor futures model with the underling asset, convenience yield, instantaneous risk free interest rate and exchange rate, is established. These processes follow jump-diffusion processes (Wiener process and Poisson process). The corresponding partial differential equation (PDE) of the futures price is derived. The general solution with parameters of the PDE is drawn. The weight least squares approach is applied to obtain the parameters of above PDE. Variance is substituted by semi-variance in Markovitz’s portfolio selection model. Therefore, a class of multi-period semi-variance model is formulated originally. A hybrid genetic algorithm (GA) with particle swarm optimizer (PSO) is proposed to solve the multi-period semi-variance model. Finally, an example, which are fuel futures in Shanghai exchange market, is selected to demonstrate the effectiveness of above models and methods.
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References
Ross, S.A.: Hedging long run commitments: Exercises in incomplete market pricing. Preliminary draft. Working paper (1995)
Schwartz, E.S.: The stochastic behavior of commodity prices: Implications for valuation and hedging. J. Finance LII, 923–973 (1997)
Gibson, R., Schwartz, E.S.: Stochastic convenience yield and the pricing of oil contingent claims. J. Finance XLV, 959–976 (1990)
Schwartz, E.S., Smith, J.E.: Short-term variations and long-term dynamics in commodity prices. Manag. Sci. 46, 893–911 (2000)
Bjerksund, P.: Contingent claims evaluation when the convenience yield is stochastic: Analytical results. Working paper (1991)
Cortazar, G., Schwartz, E.S.: The evaluation of commodity contigent claims. J. Deriv. 4, 27–39 (1994)
Merton, R.C.: Continuous-Time Finance. Blackwell, Cambridge (1990)
Jarrow, R.A., Rudd, A.: Option Pricing. Irwin, Homewood (1983)
Cox, J.C., Ross, S.A.: The valuation of options for alternation stochastic process. J. Financ. Econ. 3, 145–166 (1985)
Cortazar, G., Schwartz, E.S.: Implementing a stochastic model for oil futures prices. Energy Econ. 25, 215–238 (2003)
Gong, G.L.: Introduction to Stochastic Differential Equations. Peking University Press, Peking (1987)
Markowitz, H.: Portfolio selection. J. Finance 7, 77–91 (1952)
Grauer, R.R., Hakansson, N.H.: On the use of mean-variance and quadratic approximations in implementing dynamic investment strategies: a comparison of returns and investment policies. Manag. Sci. 39, 856–871 (1993)
Hakansson, N.H.: Multi-period mean-variance analysis: toward a general theory of portfolio choice. J. Finance 26, 857–884 (1971)
Mossin, J.: Optimal multiperiod portfolio policies. J. Bus. 41, 215–229 (1968)
Pliska, S.R.: Introduction to Mathematical Finance. Blackwell, Malden (1997)
Samuelson, P.A.: Lifetime portfolio selection by dynamic stochastic programming. Rev. Econ. Stat. 51, 239–246 (1969)
Markowitz, H.: Portfolio Selection. Wiley, New York (1959)
Lanzilotti, R.F.: Pricing objectives in large companies. Am. Econ. Rev. 48, 921–940 (1958)
Swalm, R.O.: Utility theory—insights into risk taking. Harvard Bus. Rcv. 44, 123–136 (1966)
Mao, J.C.T.: Survey of capital budgeting: theory and practice. J. Finance 25, 349–360 (1970)
Petty, J.W., Scott, D.F., Monroe, M.B.: The capital expenditure decision-making process of large corporations. Eng. Econ. 20, 159–172 (1975)
Mao, J.C.T.: Models of capital budgeting, E-V versus E-S. J. Financ. Quant. Anal. 4, 557–675 (1970)
Hogar, W.W., Warren, J.M.: Toward the development of an equilibrium capital market model based on semivariance. J. Financ. Quant. Anal. 9, 1–11 (1974)
Bilchev, G., Parmer, I.C.: The ant colony metaphor for searching continuous design spaces. In: Proceedings of the AISB Workshop on Evolutionary Computation, University of Sheffield, UK, 3–4 April 1995
Lin, Y., Ma, L., Zhang, J.J.: Reactive power optimization by GA/SA/TS combined algorithms. Electr. Power Energy Syst. 24, 765–759 (2002)
Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of IEEE Conference on Neural Networks, vol. IV, Poscataway, NJ, pp. 1942–1948 (1995)
Krohling, R.A.: Gaussian swarm: A novel particle swarm optimization algorithm. In: Proceedings of the 2004 IEEE Conference on Cybernetics and Intelligent Systems, Singapore, 1–3 December, 2004
Angeline, P.J.: Evolutionary optimization versus particle swarm optimization: philosophy and performance differences. Evol. Program. 7, 601–610 (1998)
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Yan, W., Li, S. A class of multi-period semi-variance portfolio selection with a four-factor futures price model. J. Appl. Math. Comput. 29, 19–34 (2009). https://doi.org/10.1007/s12190-008-0086-8
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DOI: https://doi.org/10.1007/s12190-008-0086-8