* Brexit deal agreement initially boosts pound
* Deal still needs parliamentary approval, doubts linger
* Domestic stocks come off highs, UK yields fall (Updates with new headline, no change to text)
By Olga Cotaga and Thyagaraju Adinarayan
LONDON, Oct 17 (Reuters) - A surge in sterling and the rally in Britain's domestically exposed stocks fizzled on Thursday as investors braced for a showdown in the UK parliament over the new Brexit deal agreed between Brussels and London.
Both sides had found a "legally operative solution" to avoid a hard border in Ireland - a key sticking point, EU chief negotiator Michel Barnier told reporters.
That sent the pound up as much as 1.1% to a five-month high and within a whisker of $1.30, while UK stocks that make most of their money at home surged.
But the gains were temporary as the Northern Irish Democratic Unionist Party (DUP), which has a deal to support British Prime Minister Boris Johnson in parliament, said it would vote against the accord at an extraordinary session on Saturday.
That revived fears that Johnson will suffer the same fate as his predecessor: a failure to get British lawmakers to support the plan for the departure, plunging the country into another round of uncertainty.
"The question now is if the UK parliament will approve the deal or not," said Athanasios Vamvakidis, global head of G10 forex strategy at BAML. Nonetheless, "in the scenario if the parliament doesn’t approve the deal, still having a deal is a good thing", he said.
Therefore, now "the risk of a no-deal Brexit is very small".
In an extraordinary Saturday sitting, the first since 1982, parliament will vote on approving British Prime Minister Boris Johnson's deal. Britain is due to leave the EU on Oct. 31.
But Johnson, whose Conservatives have no majority in the 650-seat House of Commons, will face a deeply divided parliament where his opponents are trying to force both a delay to Brexit and another referendum.
"Amid the optimism ... as things stand, parliamentary ratification is far from certain," Dean Turner, an economist at UBS, said.
The pound was up 0.2%% at $1.2853 by 1520 GMT - far below the five-month high og $1.2988 it touched earlier in the day.
Sterling has been on a rollercoaster ride, and is up 7% since early September when it hit the lowest since October 2016 at $1.19.
Volatility expectations for sterling over the next week have jumped to their highest since the 2016 Brexit referendum.
Against the euro, sterling rose 0.2%% to 86.52 pence, having earlier reached 85.77 pence.
The UK's FTSE mid-cap stocks index was well off its day's high and was last trading up 0.3%. The blue-chip exporter-heavy FTSE 100 index rose 0.5% on sterling's reversal.
British government bond yields initially surged, with 10-year yields hitting 0.79%, their highest since July , before falling slightly on the day to 0.69%.
The agreement on a deal, while still to face a parliamentary test, has triggered a rethink on the outlook for UK stocks.
JPMorgan's basket of London-listed companies that make their cash at home has enjoyed a meteoric rally in the past week.
In this period it has vastly outperformed the FTSE 100 and FTSE 250. The benchmark is considered a barometer of Brexit worries.
Optimism that a Brexit deal would be finalised saw money markets reduce expectations of rate cuts from the Bank of England. They now see a 60% chance of a quarter point cut next December versus 76% on Tuesday and 90% last week.
Euro zone money markets too priced out chances of a year-end rate cut
Writing by Tommy Wilkes Additional reporting by Saikat Chatterjee, Josephine Mason, Joice Alves and Yoruk Bahceli; Editing by Sujata Rao and Alison Williams