Financial derivatives and Lie symmetries

K. Charalambous, P. G.L. Leach

Research output: Contribution to journalArticlepeer-review


Derivatives in finance have become pervasive in recent decades. Tremendous impetus was given to this aspect of finance by the pioneering papers of Black and Scholes (1973) and Merton (1973) and has attracted considerable interest since. In general the evolution partial differential equations were solved by means of the traditional methods of partial differential equations and by ansatz previously useful in similar contexts. Here we illustrate the benefits of an algorithmic approach using the method of symmetry analysis introduced by Sophus Lie in the nineteenth century. We demonstrate the utility of this analytic approach with several examples chosen from the field of financial mathematics.

Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalTransactions of the Royal Society of South Africa
Issue number1
Publication statusPublished - 2015


  • Evolution partial differential equations
  • Financial mathematics
  • Lie symmetries


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