Generalized Exchange Option Pricing and Empirical Analysis Based on Asset Liquidity Risk

In this paper, we integrate liquidity risk into the generalized exchange option pricing model. Based on Esscher’s transformation theory, we calculate the expectation and variance of random variables to derive an explicit expression of the generalized exchange option pricing formula considering the liquidity risk of underlying assets, which avoids the complicated calculation of the optimal parameter vector h*. In addition, we plot time-series liquidity curves to screen underlying stocks that fit the model framework, and employ the simulated annealing algorithm to estimate model parameters based on historical data. Finally, numerical simulations are conducted with the estimated parameters and actual market data as inputs, confirming the internal consistency of the model. Relevant parameters are then adjusted to intuitively illustrate how liquidity risk affects option pricing and the associated price movements.