International Consolidated Airlines (LSE:IAG) shares remain extremely volatile. They’re up 9% over the last month, but remain 7% lower since the start of the year as the Middle East conflict rolls on.

The Iran war has significant implications for airline stocks, from route disruptions to soaring costs. News on the conflict has been more encouraging in recent hours — Iran has signalled today (6 May) that the Strait of Hormuz could be reopened as the US pauses military operations.

IAG’s share price has risen on the news. But I’m not tempted to buy the FTSE 100 company. In fact, I’ve found 13,000 more reasons to avoid the British Airways owner today.

So what’s happened?

So far in May, airlines have cancelled 13,000 flights to conserve fuel and reduce costs. That’s according to aviation analytics company Cirium. Since the conflict began in February, jet fuel prices have doubled, as oil supply disruption has decimated fuel stocks.

IAG’s carriers like Aer Lingus, Iberia, and British Airways haven’t changed their schedules yet. But it’s a very real possibility in the weeks ahead as the Strait of Hormuz remains closed and a breakthrough on a lasting ceasefire remains elusive.

Of all of the world’s major airline operators, IAG could be especially impacted by fuel supply shortages, too. Why? The UK imports around two-thirds of the jet fuel it uses, reflecting the closures of major refineries in recent years. And the FTSE 100 firm generates substantial profits from its British bases, such as Heathrow where it controls around half of the London airport’s take-off and landing slots.

What next?

A Middle East ceasefire should put these fears to bed. The problem for me as an investor is progress on a peace plan remains difficult.

Senior market analyst Daniela Hathorn of Capital.com notes that

many key details remain unresolved, and past experience has shown that negotiations can quickly stall or reverse. Internal divisions within Iran, in particular, remain a potential obstacle to a smooth agreement.

It’s not just the impact of flight disruptions and soaring fuel costs that concern me, as significant as they are. Other consequences of the conflict are rising inflation and cooling economic growth, both of which threaten demand for discretionary items like holidays.

In the UK, consumer confidence has plunged to three-year lows. The same downward trend is being witnessed in other key markets like North America and Europe.

Here’s what I’m doing

There is one crumb of comfort for IAG, however. Through Aer Lingus and Vueling, it has exposure to the budget aviation market. The result? Demand across these carriers could rise if travellers choose cheaper services, or if they prioritise short-haul trips.

But this isn’t a guarantee, and it may not come close to offsetting damage elsewhere to the group. Long-haul travel — and especially transatlantic routes — are essential profit drivers for IAG. What’s more, the company has been working to increase the share of premium seats it offers. This could backfire spectacularly in the current climate.

Today IAG shares trade on a forward price-to-earnings (P/E) ratio of 6.9 times. That’s above the 10-year average of roughly five times, and is a premium that (in my view) doesn’t reflect the huge dangers it currently faces. So I’m looking for other stocks to buy.