Why is katana so expensive?

Could you please elaborate on why the katana, a traditional Japanese sword, commands such a high price in the market? Are there specific factors, such as the craftsmanship, materials used, or historical significance, that contribute to its steep valuation? Additionally, how does the demand for katana compare to its limited supply, and does this imbalance play a role in driving up its price? Lastly, what are some of the challenges or considerations that buyers should be aware of when purchasing a katana to ensure they are getting a genuine and valuable piece?