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Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance

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  • Khalique, Chaudry Masood
  • Motsepa, Tanki

Abstract

The one-factor term structure model by Vasicek is analysed from the point of view of Lie symmetry analysis. Its one-parameter Lie point symmetries and corresponding group of adjoint representations are obtained. An optimal system of one-dimensional subalgebras is derived and is then used to obtain symmetry reductions and group-invariant solutions. The group-invariant solutions presented here are new and have not appeared in the literature. Moreover, we derive conservation laws for the Vasicek equation by employing the theorem due to Ibragimov.

Suggested Citation

  • Khalique, Chaudry Masood & Motsepa, Tanki, 2018. "Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 871-879.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:871-879
    DOI: 10.1016/j.physa.2018.03.053
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
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    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Lie symmetry analysis, explicit solutions and conservation laws for the space–time fractional nonlinear evolution equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 371-383.
    7. Inc, Mustafa & Yusuf, Abdullahi & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 94-106.
    8. Saberi, Elaheh & Reza Hejazi, S., 2018. "Lie symmetry analysis, conservation laws and exact solutions of the time-fractional generalized Hirota–Satsuma coupled KdV system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 296-307.
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