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

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...

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Bibliographic Details
Published in:Applied economics 2021-06, Vol.53 (29), p.3391-3407
Main Authors: Lee, Kyungsub, Seo, Byoung Ki
Format: Article
Language:English
Subjects:
delta hedging
Economic analysis
Economic theory
European option
limit order
Liquidity
Liquidity cost
Monte Carlo simulation
Multiplication
Prices
quadratic variation
Securities prices
Simulation
Stock prices
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Summary: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.
ISSN:0003-6846
1466-4283
DOI:10.1080/00036846.2021.1881430