ParamViewModel.kt

class ParamViewModel(
    someParameter: Int
) : ViewModel() {

}

SomeActivity.kt

class SomeActivity : FragmentActivity() {

    private lateinit var viewModel: ParamViewModel

    override fun onCreate(savedInstanceState: Bundle?) {
        ...
        val param = 42
        val factory = ParamViewModelFactory(param)
        viewModel = ViewModelProviders.of(this, factory).get(ParamViewModel::class.java)
        ...
    }
}

ViewModelFactory.kt

class ParamViewModelFactory(
    private val someParameter: Int
) : ViewModelProvider.NewInstanceFactory() {

    override fun <T : ViewModel> create(modelClass: Class<T>): T {
        return ParamViewModel(someParameter) as T
    }
}