We propose a modification of an option pricing model which was recently introduced by Borland. The original model leads to underlying stock price processes which are Markovian with Tsallis-distributed rates of return. We show that the closed-form option pricing formulas that are derived in this model admit explicit arbitrage opportunities.
In order to specify a correct model, we prove existence and uniqueness of a strong solution for a certain degenerate stochastic differential equation. We then show that a Girsanov transformation can be applied which enables us to develop practical option pricing algorithms in terms of partial differential equations, which are guaranteed to be free of arbitrage.