Pound gains from optimism over US-Iran deal, options suggest calm after local elections 

* Local elections eyed, Labour faces possible leadership change

* Sterling gains despite ​flat economy, ⁠rising inflation

* Options market shows muted volatility expectations for pound ​around elections

LONDON, May 6 (Reuters) - The pound rose against the dollar on Wednesday, as investors took heart from an Axios report saying that ​the ‌United States and Iran were closing in on a deal to end the war.

In Britain, key local elections take place ⁠on Thursday and Prime Minister Keir Starmer's Labour Party is bracing ⁠for big losses. Repeated scandals and criticism ​that it has not yet delivered an improvement in living standards have stirred speculation Starmer may be replaced, a cause for concern for investors in the bond and currency markets.

Prediction market site Polymarket shows there is a near-70% chance Starmer ​will be ‌out by December. That has risen from a low probability of 49% in early April.

Sterling was last up 0.6% on the day at $1.3621 around its highest since February. Against the euro, the pound was steady, leaving the single currency at 86.35 pence.

"More political instability could be on its way and investors could well be ​positioning for the potential for renewed political instability that could follow Thursday’s local elections," MUFG currency strategist .

The pound has ‌gained nearly 7% since Labour won the 2024 general election and benchmark interest rates are at 3.75%, down from 5.25%.

But the economy is flatlining, inflation is ‌starting to flare as energy prices surge due to the U.S-Iran conflict, and borrowing costs for anything from a mortgage to personal loans have risen to multi-year highs, as gilt yields have risen.

Five-year gilts yield was around 4.53%, ​having jumped from 3.68% before the war broke out in late February and they are up from 4.05%, when Labour came to ‌power.

A survey of monthly business activity showed UK services firms witnessed the largest rise in price pressures in three and a half years in April, with more than half of the respondents reporting an increase in their average ⁠cost burdens.

Meanwhile, ⁠the options market painted a fairly sanguine picture for the election, as ‌the cost of protection against big overnight swings in the pound fell in line with that for other major currencies.

Overnight implied volatility, one measure ​of the cost of hedging ​against big moves in the pound over a 24-hour period, drifted to around ‌6.83%, roughly in the middle of its recent range. Overnight implied vol for euro/sterling, meanwhile, was also relatively subdued at 2.71%, according to LSEG data.

A week ago, the cost of hedging against a big move after Thursday's election was around 6.27%.