偏态布朗运动不应作为风险中性收益过程：一个适定的偏正态替代方案
The skew Brownian motion should not be used as a risk-neutral returns process: a well-posed skew-normal alternative
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中文总结 AI 辅助
本文指出基于偏态布朗运动的风险中性收益模型存在套利且基础有误，提出适定的偏正态替代方案，重述期权定价公式并证明其无套利，给出渐近分析和随机占优性质。
中文摘要 AI 辅助
基于偏态布朗运动（SBM）的风险中性金融估值收益模型约在二十年前被引入，近年来日益流行。遗憾的是，其发展背后的故事充满错误和误解，首先源于基础性误述，即流行的金融模型基于Itô-McKean SBM——而事实上并非如此。此外，更严重的是，rossello2012arbitrage关于收益中带局部时间的价格模型（如SBM）存在套利机会的澄清在很大程度上被忽视了。本文试图通过揭露迄今为止我们所能追溯到的所有错误，清除现有关于SBM的期权定价文献中潜伏的混淆和误解。然而，认识到SBM偏正态边际在风险中性估值中的潜力，作为积极贡献，我们重新表述了所谓的SBM看涨期权定价公式，并表明即使SBM收益模型存在套利，其期权定价公式并不存在套利。随后，我们确定了具有偏正态边际的正确马尔可夫随机微分方程，证明了其强适定性，并利用闭式公式的可用性，对隐含波动率曲面进行了渐近分析。在得出结论的过程中，我们获得了一个独立的、具有独立意义的正态/偏正态随机占优性质。
英文摘要
Return models for risk-neutral financial valuation based on skew Brownian motions (SBMs) have been introduced about twenty years ago, and have recently enjoying growing popularity. Unfortunately, the story behind their development is one of mistakes and erroneous interpretations, beginning from the foundational misrepresentations that the prevalent financial model is based on the Itô-McKean SBM -- which, in fact, it is not. Besides, and more seriously, the clarification of \cite{rossello2012arbitrage} that price models with a local time in their returns, such as the SBM, are arbitrageable has been, by and large, ignored. In this paper, we try to clear the field from the confusions and misconceptions lurking in the standing option pricing literature on SBM, by exposing all the errors we could trace in the treatment so far. Recognizing however the potential of the SBM skew-normal marginals for risk-neutral valuation, as a positive contribution, we reformulate the putative SBM call pricing formula and show that, even if the SBM return model admits arbitrage, its option pricing formula does not. The correct Markovian SDE with skew-normal marginals is then identified, its strong well-posedness shown, and by exploiting the availability of closed formulae, an asymptotic analysis of the implied volatility surface is offered. En route to our conclusions, we obtain a novel normal/skew-normal stochastic dominance property of independent interest.
