论文标题
Dirac交互图片的应用到选项定价
An Application of Dirac's Interaction Picture to Option Pricing
论文作者
论文摘要
在本文中，在存在时间依赖的套利气泡的情况下，将狄拉克的量子机械相互作用图片应用于选项定价，以获取黑色 - choles方程的解决方案。特别是，对于正方形气泡扰动的调用，用三个最初的希腊人（delta，gamma和速度）给出了近似解决方案（在扰动系列中有效上升三阶）。然后，根据所有高阶$ s $衍生品的黑色 - chcholes公式构建精确的解决方案。还表明，在离散的转换下，相互作用的黑色 - choles方程是不变的，该转换与基础资产的平均值互换，反之亦然。这意味着相互作用的黑色 - choles方程可以以“低能”和“高能”形式编写，以使低能形式的高相互作用极限对应于高能形式的弱交互极限。可以将扰动分析应用于高能量形式，以研究低能形式的高相互作用极限。
In this paper, the Dirac's quantum mechanical interaction picture is applied to option pricing to obtain a solution of the Black-Scholes equation in the presence of a time-dependent arbitrage bubble. In particular, for the case of a call perturbed by a square bubble, an approximate solution (valid up third order in a perturbation series) is given in terms of the three first Greeks: Delta, Gamma, and Speed. Then an exact solution is constructed in terms of all higher order $S$-derivatives of the Black-Scholes formula. It is also shown that the interacting Black-Scholes equation is invariant under a discrete transformation that interchanges the interest rate with the mean of the underlying asset and vice versa. This implies that the interacting Black-Scholes equation can be written in a 'low energy' and a 'high energy' form, in such a way that the high-interaction limit of the low energy form corresponds to the weak-interaction limit of the high energy form. One can apply a perturbative analysis to the high energy form to study the high-interaction limit of the low energy form.
