On the multiplicity of option prices under CEV with positive elasticity of variance

The discounted stock price under the Constant Elasticity of Variance (CEV) model is a strict local martingale when the elasticity of variance is positive. Two expressions for the European call price then arise, namely the risk-neutral call price and an alternative price that is linked to the unique put price via the put-call parity. The analytical tractability of the CEV model is first exploited to intuitively and formally discuss the properties of the stock price distribution. The subsequent discussion of the sensitivity of the three option prices to their underlying parameters illustrates that the Greeks of the risk-neutral call price can differ considerably from the familiar relations and as such offer additional tools for the detection of asset-price bubbles.