Following are the features of corticospinal involvement except
Babinski sign is the sure sign of pyramidal tract/corticospinal lesion.
Spasticity and exaggerated tendon reflexes are due to extrapyramidal lesions. 
Since pyramidal lesion occurring alone is rare, extrapyramidal lesions also may be seen. Rigidity seen is clasp knife type.
Cog-wheel rigidity
Spasticity
Plantar extensor response
Exaggerated deep tendon reflexes