Which ATM option has the most vega

Three at-the-money options on different underlyings share the same expiry $T$; their strikes are $10$, $20$ and $30$. Under Black-Scholes assumptions (same volatility and rate), which one has the greatest vega?

The strike-30 option. Black-Scholes vega is $S\,\varphi(d_1)\sqrt{T}$. At the money $S=K$ and $d_1$ is the same for all three, so vega scales linearly with the price level and is largest for the option with $S=K=30$.