The discounted price process under the constant elasticity of variance (CEV) model is not a martingale (wrt the risk-neutral measure) for options markets with upward sloping implied volatility smiles. The loss of the martingale property implies the existence of (at least) two option prices for the call option: the price for which the put-call parity holds and the (risk-neutral) price representing the lowest cost of replicating the call payoff. This article derives closed-form solutions for the Greeks of the risk-neutral call option pricing solution that are valid for any CEV process exhibiting forward skew volatility smile patterns. Using an extensive numerical analysis, we conclude that the differences between the call prices and Greeks of both solutions are substantial, which might yield significant errors of analysis for pricing and hedging purposes.

中文翻译：

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有关CEV模式下期权和泡沫的注释：对定价和对冲的影响

对于具有向上倾斜隐含波动率微笑的期权市场，在恒定方差弹性（CEV）模型下的折价过程不是a（折衷为风险中性度量）。the资产的损失意味着看涨期权存在（至少）两个期权价格：看跌期权平价持有的价格和（风险中性）价格表示复制看涨收益的最低成本。本文为风险中立的看涨期权定价解决方案的希腊文提供了封闭式解决方案，该解决方案适用于任何表现出前斜率波动微笑模式的CEV过程。通过广泛的数值分析，我们得出结论，两种解决方案的通话价格和希腊字母之间的差异都很大，