Analytic formula for option margin with liquidity costs under dynamic delta hedging

Kyungsub Lee, Byoung Ki Seo
2021 Applied Economics  
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
more » ... ost 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.
doi:10.1080/00036846.2021.1881430 fatcat:hgvf6g7r3jellitba65cpthis4