Binomial jump-amplitude modeling in SDEs: A regularized stepwise estimation with computational diagnostics

The presence of the jump process makes parameter estimation for stationary stochastic differential equations particularly challenging. Moreover, existing jump parameter models often suffer from significant systematic errors. This paper introduces a new stationary stochastic differential equation model with jumps, in which the jump amplitude follows a binomial distribution. This approach helps mitigate systematic errors, particularly those arising when the probability density remains nonzero for infinitely large jump amplitudes or when it becomes excessively high at zero jump size. On this basis, we use the stepwise estimation method to estimate the parameters of the model (that is, first estimate parameters of the drift and diffusion term by the tool of quadratic variation, and then estimate the parameters of the jump process), and the result has a high estimation accuracy.