On non-uniqueness in the option valuation problem

Abstract

It is known that the value of a call option in the case of constant elasticity processes (CEV) with the indicator $\hat{I}\pm$ exceeding the critical $\hat{I}\pm =1$ is determined in a non-unique way. We show how, based on an already existing mathematical theory concerning the correctness of boundary conditions for degenerate parabolic equations on the semi-axis $[0,\infty )$, this phenomenon can be explained. Namely, for $1<\hat{I}\pm \le \frac{3}{2}$ the non-uniqueness is due to the fact that the initial data of the call option are outside the Täcklind class, and for $\hat{I}\pm >\frac{3}{2}$ it is due to the absence boundary condition for $x=\infty$.

9 pages