Pricing spread option with liquidity adjustments
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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.