论文标题
经典选择定价和一些步骤
Classical Option Pricing and Some Steps Further
论文作者
论文摘要
本文将资产价格p视为c = pv的价值C与执行交易的卷V之间的关系，并研究了该定义对期权定价方程的后果。我们表明，经典的BSM模型隐含地假设交易的值C和体积V遵循相同的Brownian过程。违反这种身份会导致二维类似BSM的方程，并具有两个恒定波动。我们表明，代理人期望那些批准交易执行的人可以进一步增加BSM模型的维度。当代理人期望可能取决于期权价格数据并表明这种假设可能导致非线性BSM样方程时，我们研究了案例。我们重新考虑了由值和体积确定的价格的赫斯顿随机波动率模型，并得出了具有随机值波动率和恒定体积波动率的3维BSM样模型。类似于BSM的方程式的多种情况指出了选项定价方程的准确性和复杂性之间合理平衡的问题。
This paper considers the asset price p as relations C=pV between the value C and the volume V of the executed transactions and studies the consequences of this definition for the option pricing equations. We show that the classical BSM model implicitly assumes that value C and volume V of transactions follow identical Brownian processes. Violation of this identity leads to 2-dimensional BSM-like equation with two constant volatilities. We show that agents expectations those approve execution of transactions can further increase the dimension of the BSM model. We study the case when agents expectations may depend on the option price data and show that such assumption can lead to the nonlinear BSM-like equations. We reconsider the Heston stochastic volatility model for the price determined by the value and the volume and derive 3-dimensional BSM-like model with stochastic value volatility and constant volume volatility. Variety of the BSM-like equations states the problem of reasonable balance between the accuracy and the complexity of the option pricing equations.
