The pan-European Stoxx 600 index was up 0.16% at midday. With most major bourses up with exception of Britain's FTSE 100, which was down slightly 0.54%.
After losing the leadership race to Liz Truss two months ago after the resignation of the disgraced Boris Johnson, 42-year-old former finance minister Sunak was officially invited to form a government by King Charles.
Sterling gained on news of Sunak's appointment and government bond yields fell below 4%.
Investors will be eyeing Finance Minister Jeremy Hunt's budget on October 31 to see how he plans to plug a £40bn black hole in Britain's public finances exacerbated by Truss’s disastrous package of unfunded tax cuts.
In his first address outside Downing Street, Sunak warned of "difficult decisions" on spending, which many fear will be the prelude to a return to the post-2008 era of austerity policies imposed by former finance minister George Osborne.
In equity news, HSBC (LON:HSBA) shares fell 7% as the bank reported a fall in third quarter earnings. Rival UBS gained after reporting a double-digit profit declines. Both institutions beat market expectations.
SAP gained despite earnings falling short of forecasts, while Softcat was up after posting higher earnings.
Online beauty products seller THG (LON:THG) surged 16% after backing its full year outlook as third-quarter revenues rose and it signed a new banking facility.
Reporting by Frank Prenesti for Sharecast.com