Bhatnagar Anantya, Vvedensky Dimitri D
The Blackett Laboratory, Imperial College London, London, SW7 2AZ UK.
Eur Phys J B. 2022;95(8):138. doi: 10.1140/epjb/s10051-022-00402-0. Epub 2022 Aug 27.
The limitations of the classical Black-Scholes model are examined by comparing calculated and actual historical prices of European call options on stocks from several sectors of the S &P 500. Persistent differences between the two prices point to an expanded model proposed by Segal and Segal (PNAS 95:4072-4075, 1988) in which information not simultaneously observable or actionable with public information can be represented by an additional pseudo-Wiener process. A real linear combination of the original and added processes leads to a commutation relation analogous to that between a boson field and its canonical momentum in quantum field theory. The resulting pricing formula for a European call option replaces the classical volatility with the norm of a complex quantity, whose imaginary part is shown to compensate for the disparity between prices obtained from the classical Black-Scholes model and actual prices of the test call options. This provides market evidence for the influence of a non-classical process on the price of a security based on non-commuting operators.
The online version contains supplementary material available at 10.1140/epjb/s10051-022-00402-0.
通过比较标准普尔500指数几个板块股票的欧式看涨期权的计算历史价格和实际历史价格，研究了经典布莱克-斯科尔斯模型的局限性。这两种价格之间的持续差异指向了西格尔和西格尔（《美国国家科学院院刊》95:4072 - 4075，1988）提出的一个扩展模型，其中不能与公共信息同时被观测到或采取行动的信息可以由一个额外的伪维纳过程来表示。原始过程和添加过程的实线性组合导致了一种对易关系，类似于量子场论中玻色子场与其正则动量之间的对易关系。由此得到的欧式看涨期权定价公式用一个复数量的模取代了经典波动率，其虚部被证明可以补偿从经典布莱克-斯科尔斯模型获得的价格与测试看涨期权实际价格之间的差异。这为基于非对易算符的非经典过程对证券价格的影响提供了市场证据。
在线版本包含可在10.1140/epjb/s10051 - 022 - 00402 - 0获取的补充材料。
