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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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:709871
    DOI: 10.1155/2014/709871
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    References listed on IDEAS

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    1. Cox, John C. & Ingersoll Junior, Jonathan E. & Ross, Stephen A., 2007. "A theory of the term structure of interest rates," RAE - Revista de Administração de Empresas, FGV-EAESP Escola de Administração de Empresas de São Paulo (Brazil), vol. 47(2), April.
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