The PlayStation Portable (PSP) can run some PS1 games natively because they share similar architecture. However, the PSP cannot emulate PS2. The PS Vita includes a dedicated processor for backward compatibility with the PSP. While the Vita runs PSP homebrew flawlessly, this does not extend to the PS2 architecture.
If you see YouTube videos or forum posts claiming otherwise, they are almost always fake, clickbait, or mislabeled. The PS Vita, even when overclocked, simply does not have enough raw processing power to emulate the complex Emotion Engine of the PS2. ps vita ps2 emulator vpk