论文标题
扩展的黑色 - chleos模型中的量子效应
Quantum effects in an expanded Black-Scholes model
论文作者
论文摘要
通过比较来自标准普尔500标准普尔500标准普尔的多个领域的股票的计算和实际历史价格的经典黑色 - choles模型的局限性。两个价格之间的持续差异表明Segal和Segal（1998）提出的扩展模型（1998年）与公共信息不同时可观察到的信息可以代表一个其他信息。原始过程和添加过程的真实线性组合导致的换向关系类似于玻色子场及其在量子场理论中的规范动量之间的关系。欧洲呼叫选项的最终定价公式用复杂数量的规范取代了经典的波动，其虚构部分被证明可以弥补从经典的黑色 - choles模型中获得的价格与测试呼叫选项的实际价格之间的差异。这为非经典过程对基于非公开运营商的安全价格的影响提供了市场证据。
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 (1998) 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.
