According to several polls, the last few days have seen a clear switch to more people voting to leave the EU on 23 June. While shares have dipped across the board, financial stocks have been hammered. Let’s look at three FTSE 100 giants and ask whether their shares have dropped to a point where the bad news seems to be priced-in.

Aviva (LSE: AV), Prudential (LSE: PRU) and Legal & General (LSE: LGEN) are mutinational behemoths. Aviva deals with the insurance, savings and investment needs of roughly 31m people around the world and is one of Europe’s leading providers of life and general insurance. Prudential has around 24m customers with one of its four business units focused on providing pensions, annuities, savings and investments in the UK and Europe. Legal & General has over 10m customers worldwide and, within Europe, has operations in France, Germany and the Netherlands.

What could happen

UK insurers currently have access to a single market of 28 countries. As things stand, they don’t need any additional authorisation to conduct business in the EU and avoid any local costs arising from these activities.

If Britain votes to end its 43-year membership next Thursday, UK insurance firms could suffer for a number of reasons. Clearly, the aforementioned ability to conduct business across borders would become more difficult. Insurers would likely need to set up costly divisions in the EU. A vote to leave could also mean all three companies would risk losing talented members of staff from the EU. Being denied access could weaken the case of investing in the UK’s insurance industry and, naturally, Britain would no longer have influence over insurance regulation in the region.

Nevertheless, there may be some benefits. For example, insurers would no longer be tied to regulations such as Solvency II (a directive that dictates the amount of capital insurance companies must hold to reduce the risk of insolvency), even if the UK ended up creating a similar rule for itself. Secondly, it might be argued that financial services in the UK would directly benefit from further Eurozone uncertainty that’s surely just around the corner (step forward, Greece). This may drive business back to these shores.

Time to be greedy?

Of course, there’s the possibility none of this will happen at all. Britain could remain in the EU and businesses operating in the financial services industry will likely breathe a huge sigh of relief on 24 June. So, given the whiff of anxiety/pessimism that’s been surrounding the markets this week, should investors do as Warren Buffet famously advised and “be greedy when others are fearful“?

Although the shares could drop further over the next few days, all three companies already trade on low price-to-earnings (P/E) ratios (Aviva: 8.3, Prudential: 10, L&G: 10) suggesting they’re relatively cheap compared to most of the stocks on the FTSE 100 and the index itself. Banking stocks such as Barclays, Lloyds and HSBC are on similar valuations for similar reasons. Moreover, they offer tempting yields (Aviva: 5.8%, Prudential: 3.5%, L&G: 6.6%), well-covered by current earnings. Whether this remains so in the event of a leave vote is another matter entirely.

Given their geographical diversification, I’m confident all three could adapt to a Brexit, despite the prevailing uncertainty. And should Britain remain in the EU, investors may look back on recent share price falls and wish they’d taken advantage.

Are there better options?

If investing in one or some of the UK's insurers seems like too much of a risk at the current time, you may want to look to other resilient FTSE 100 giants for safety.

Not sure where to start? The experts at the Motley Fool are here to help. They've produced a special FREE report that focuses on a group of strong, dependable businesses with consistent earnings. While a Brexit could still generate share price movements in any of these companies, their global reach means they're well positioned to ride out the expected volatility. Indeed, now might even be a perfect time to buy their shares if you plan on holding them for the long term to support your retirement.

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Paul Summers owns shares in Aviva. The Motley Fool UK has no position in any of the shares mentioned. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.