How much would a WW2-era Japanese officer samurai sword sell for today?

So my grandfather was a major in the U.S. Marine Corps and fought against the Japanese in the Pacific Theater, including the battles at Tarawa, Guadalcanal, and Saipan, among others. In one of these battles, his Marines overran a Japanese encampment and killed them all. Subsequently, he collected a katana from a dead Japanese officer-which came into my parents' possession sometime after my grandfather passed away, and the sword has hung in their house ever since.
We have no intention of ever selling this sword due to it being a family heirloom at this point, but my curiosity got the best of me recently and I wanted to find out-how much would such a sword realistically sell for as a collectible antique? I really have no idea, although my dad (who rarely speaks of his father's war exploits) once commented that "it would likely go for a lot of money." It's a bit dulled and there's a few spots of rust & wear-and possibly a bloodstain from what I can tell-but it's overall in excellent condition. It does appear to be a legitimate katana that would have been used for ceremonial purposes & possibly executions.

Thanks!