A Tower Local Controller reported a VFR aircraft overshot the final approach course into confliction with VFR traffic on the parallel runway resulting in a NMAC.

Narrative

Aircraft X was approaching a 2nm final for Runway XXR; cleared for the option. Aircraft Y was about to turn a 2nm left base for Runway XXL. I issued Aircraft Y the traffic information about Aircraft X. Aircraft Y reported traffic in sight. I issued Aircraft X traffic information about Aircraft Y. Aircraft X reported traffic in sight. About 30 seconds to 1 minute later Aircraft X reported that Aircraft Y almost ran into him on final and that he had to deviate off of his approach. He stated that Aircraft Y was about 20 ft. away from him. Aircraft X rejoined final; completed his touch and go; on Runway XXR and Aircraft Y landed safely on Runway XXL. After landing Aircraft Y reported that his student took the aircraft through final and he did not recover in time; but he estimated that he was about 200 ft. away from Aircraft X. Although this event was not ideal; this is how a Class D airspace and parallel Runways work with 2 VFR aircraft. Appropriate traffic information was exchanged between the two aircraft; they had each other in sight; and saw and avoided. If Aircraft X is correct about only having 20 ft. between him and the parallel traffic; separation was still not lost. The only way to fully correct this at ZZZ would be to either fully eliminate simultaneous parallel runway operations or change our class of airspace to require more stringent separation.