Volatility, a measure of options demand, for options that allow the holder to buy Brent futures between $75 and $80 a barrel, has risen this week above 30 percent to its highest since late 2016.

Iran pumped nearly 4 percent of world crude oil in March, according to the International Energy Agency. The options market shows that in the last month, investors have bought more than twice as many calls at $75, $80 and $85 that expire in late May than any other option maturing at that time.

Open interest in $75, $80 and $85 May calls has risen by nearly 60,000 lots in the last month, and almost 10,000 of that total has been added in the last five days alone.

(Graphic: July Brent crude options open interest, https://reut.rs/2J4l5Eu)

Volatility for options that are "at the money", or roughly around the current futures price, is below 25 percent.

Oil has risen 7 percent so far this year, making it one of the best-performing commodities and one of the few financial assets to turn a profit in 2018. In comparison, U.S. blue-chip stocks have shown no change and palladium has lost more than 8 percent.

Oil analysts have grown more optimistic on the prospects of a sustained rally. Those surveyed in the Reuters monthly price poll have raised their forecasts for Brent and WTI every month since last August. [O/POLL]

(Graphic: Oil analysts grow more bullish as Iran tensions rise, https://reut.rs/2H93f2l)

The case for a higher oil price has been in place for some time, illustrated by discipline in maintaining crude output cuts among some of the world's largest suppliers, record levels of fund interest and robust demand growth.

The Organization of the Petroleum Exporting Countries and 10 of its partners have withheld 1.8 million barrels per day (bpd) in oil production since January 2017 and succeeded in cutting a vast global overhang of unused crude and refined products.

Yet it has been geopolitical developments that have helped oil vault above $70 a barrel, starting with the appointment by U.S. President Donald Trump of policy hawks such as John Bolton as national security advisor and Mike Pompeo as secretary of state.

Trump has warned that the United States will pull out of a nuclear deal between Iran and six majors powers by May 12 unless Congress and European allies help "fix" it with a follow-up agreement.

(Graphic: Google searches for "Iranian sanctions", https://reut.rs/2vp2yAM)

In the last two weeks alone, a number of investment banks including Julius Baer, BNP Paribas and Barclays have raised their price forecasts and cited Iran as a key reason.

Societe Generale said on April 5 it saw a 70 percent chance of Iran oil sanctions snapping back into effect in May.

This could remove up to 500,000 bpd of production and add $10 to the oil price, Societe Generale said, adding that of that $10, $5 was already priced in.

Goldman Sachs said the potential partial loss of Iranian output could add $7 to the price.

"With low and declining inventories, the market remains vulnerable to even small disruptions," it said.

(Graphic: Brent crude options volatility surface, https://reut.rs/2EQ1cOZ)

(Reporting by Amanda Cooper; Editing by Dale Hudson)

By Amanda Cooper