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Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

Author

Listed:
  • Tanki Motsepa
  • Chaudry Masood Khalique
  • Motlatsi Molati

Abstract

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

Suggested Citation

  • Tanki Motsepa & Chaudry Masood Khalique & Motlatsi Molati, 2014. "Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, April.
    • Handle: RePEc:hin:jnlaaa:709871
    DOI: 10.1155/2014/709871
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    Cited by:

    1. Andronikos Paliathanasis & K. Krishnakumar & K.M. Tamizhmani & Peter G.L. Leach, 2016. "Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility," Mathematics, MDPI, vol. 4(2), pages 1-14, May.

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