ABSTRACT

This study derives the expected liquidity cost when performing the delta hedging process of a European option. This cost is represented by an integration formula that includes European option prices and a certain function depending on the delta process. We first define a unit liquidity cost and then show that the liquidity cost is a multiplication of the unit liquidity cost, stock price, supply curve parameter, and the square of the number of options. Using this formula, the expected liquidity cost before hedging can be calculated much faster than when using a Monte Carlo simulation. Numerically computed distributions of liquidity costs in special cases are also provided.

摘要

本研究得出执行欧式期权的 delta 对冲过程时的预期流动性成本。该成本由一个积分公式表示，该公式包括欧式期权价格和取决于 delta 过程的特定函数。我们首先定义单位流动性成本，然后证明流动性成本是单位流动性成本、股票价格、供给曲线参数和期权数量平方的乘积。使用此公式，可以比使用蒙特卡罗模拟更快地计算对冲前的预期流动性成本。还提供了特殊情况下流动性成本的数值计算分布。