Pricing spread option with liquidity adjustments

TL;DR

This paper investigates the pricing and hedging of European spread options considering market liquidity impacts, introducing models that account for how trading strategies influence stock prices and affect option valuation.

Contribution

It develops generalized Black-Scholes PDEs incorporating liquidity effects and compares full-impact and partial-impact models, highlighting their influence on option pricing and hedging strategies.

Findings

Full impact model results in higher option prices.

Liquidity effects cause traders to buy more stock for replication.

Illiquidity significantly affects hedging strategies.

Abstract

We study the pricing and hedging of European spread options on correlated assets when, in contrast to the standard framework and consistent with imperfect liquidity markets, the trading in the stock market has a direct impact on stocks prices. We consider a partial-impact and a full-impact model in which the price impact is caused by every trading strategy in the market. The generalized Black-Scholes pricing partial differential equations (PDEs) are obtained and analysed. We perform a numerical analysis to exhibit the illiquidity effect on the replication strategy of the European spread option. Compared to the Black-Scholes model or a partial impact model, the trader in the full impact model buys more stock to replicate the option, and this leads to a higher option price.