Digital power generalized exchange option pricing considering liquidity risk

Traditional option pricing models mostly assume that the market is frictionless, ignoring the impact of liquidity on option price. In response, this paper considers a digital power generalized exchange option pricing problem when the underlying asset has liquidity risk. We obtained a closed-form digital power option pricing formula in a incomplete market by measure transformation. Finally, numerical experiments were conducted by comparing the prices computed by the new formula with those from Monte-Carlo simulations, thereby validating the accuracy of the new formula. Building on this, the impact of liquidity on option prices was further investigated.