Jarrow and co find a better way to spot stock market bubbles

Quant team’s options-based approach avoids pitfalls of historical data dependence

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As analysts warn about euphoria in US markets and the Cape ratio – economist Robert Shiller’s widely watched metric of stock market frothiness – nears all-time highs, investors could do with a reliable way to detect and measure asset bubbles.

As a matter of course, buy-siders weigh prices against model-derived reference points of fundamental value. But their reliance on historic data can leave these models open to question – especially when conditions change rapidly, as they have this past year. And now a team of academic quants from two US universities has come up with what they claim to be a better approach.

“We don’t rely on past data at all,” says Nicola Fusari, assistant professor at Johns Hopkins Carey Business School and one of the three-man team that has developed a method of detecting bubbles that instead uses data from options markets.

It’s an illustrious team, in which Fusari and his colleague, post-doctoral fellow Sujan Lamichhane, are joined by Robert Jarrow – the Cornell University professor and veteran of financial mathematics whose pricing models are among those used as standard in the derivatives industry.

The gauge they have developed could give early warnings of growing speculation, says Fusari, such as the boom in GameStop stock seen in January, when the company’s shares climbed 2,000% before collapsing amid general chaos. It could also help distinguish between frothiness and bona fide growth in stocks that experience each at different times.

We don’t rely on past data at all
Nicola Fusari, Johns Hopkins Carey Business School

The researchers’ idea is to calibrate an options pricing model using market prices from put options and use the model to generate ‘fair value’ prices for equivalent call options. By measuring the difference between the model-generated and actual market prices for calls, the team says it can identify bubbles and determine their scale.

More conventional bubble indicators that model fair value using past data can sometimes miss structural shifts that might justify a rise in prices – shifts such as lower interest rates or behavioural changes like a rise in online shopping – and backward-looking data can also pick up the effects of a bubble already underway.

Why it works

The new approach works because of differences in how buyers price put and call options, says Fusari. Puts, which protect against falling prices, are unaffected by speculative bubbles in underlying assets, he adds. Their payoff is capped at the strike price, while call options with their unlimited payoffs “inherit” the price increases of a bubble in their underlying assets.

Investors in essence base the pricing of put options on what they think an asset is worth. But they price calls based on where they think the asset will sell. The differences can reveal how far investors are ignoring fundamentals and engaging in pure speculation, says Fusari.

The indicator picked up the bubble long before GameStop got the attention of the media
Nicola Fusari

The new indicator would have shown a bubble was building in GameStop stock as early as late December, when the price was still below $50 a share, he adds.

“The indicator picked up the bubble long before GameStop got the attention of the media,” says Fusari. GameStop’s closing price reached $347 on January 27, by which time the price was almost wholly due to speculation.

The indicator could show when big price jumps are justified – and when they’re not. Amazon’s share price more than doubled in 2016 and 2017, but the indicator pointed to no significant bubbles during that time. By contrast, bubbles in Amazon stock reached as high as 20% in 2015 and 2018, and bubbles greater than 10% were “numerous”, say the academics.

A new skew

Some investment firms already use option pricing signals, though not usually in the same way. Tracking option skew — the difference between implied volatility on puts versus calls — is a common method.

“How much higher implied volatility is on puts versus calls gives you a read on how much demand there is for protection versus upside optionality,” says Christopher Reeve, director of risk at Aspect Capital. “Which could give you a view on how scared people are about a particular asset.”

The new approach, however, explains divergence in the pricing of puts versus calls as a function of speculative buying, rather than assuming such differences arise from market frictions and heavier buying of one or other instrument. By implication, the new model can indicate not only whether assets are frothy, but how frothy they are.

One buy-side quant says his firm has used similar ideas and found them to be useful. But options data can be spotty, which has held back wide adoption of this kind of approach, he points out.

The quants first proposed the idea last year but updated their research in February after testing the effectiveness of the gauge on the GameStop episode. According to Fusari, they now plan to test their approach further, applying it in different markets and over multiple time periods.

Assuming results are positive, investors will no doubt want to test the idea too. The swift recovery in markets has fuelled concerns that valuations are too high. But low interest rates, fiscal stimulus and the post-Covid economic recovery point to further market gains, leaving investors uncertain how to proceed.

According to Farouk Jivraj, a visiting researcher at Imperial College Business School, who worked with Shiller on a revision of his market valuations indicator last year, conflicting forces are at play. “Investors are worried that now may be the wrong time to buy,” he says. “But they’re also worried about missing out if they don’t.”

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