Traders and energy companies risk costly mistakes when pricing commodity derivatives—financial contracts tied to oil, gas, and other commodities—if they overlook a market phenomenon known as the Samuelson effect, according to new research by a Johns Hopkins mathematician. Published in the Multidisciplinary Digital Publishing Institute (MDPI) journal, the study offers a practical, data-driven model that helps account for this effect, offering a clearer path to more accurate pricing and improved risk management.
Roza Galeeva, senior lecturer in the Whiting School of Engineering’s Department of Applied Mathematics and Statistics, has long studied a well-known phenomenon in commodities futures: that price volatility tends to rise sharply as contracts approach their expiration dates. Known as the Samuelson effect, this pattern is widely recognized by both experienced commodity traders and market analysts.
“People sometimes try to use the same models they use for stocks,” said Galeeva. “But commodities behave differently–you’re dealing with real physical goods, not just paper assets.”
Her research, developed through years of academic and industry work—including projects with graduate students at NYU and later at Johns Hopkins—proposes a practical solution. It focuses on how the value of commodity derivatives depends not just on the total realized variance of the underlying commodity, but also on the way that variance accumulates over time—an especially important factor for pricing path-dependent options.
“Think of variance as a clock,” she said. “At the start of a contract, time moves slowly. But as you get closer to expiration, things speed up. That’s how variance behaves—and that is how, through modeling of a clock with exponential decay, we capture the phenomenon.”
Galeeva’s approach relies on historical market data and can be efficiently calibrated, making it useful for practitioners who need fast, accurate pricing tools.
She tested the model using this data and ran it through a robust calibration process, using statistical tests—similar to machine learning techniques—to confirm its accuracy. Testing revealed that the model delivered dependable results within industry standards.
“This isn’t just theoretical. We tested it with historical data,” said Galeeva. “It holds up—and it’s easy to update as markets evolve.”
The model can be applied to renewable energy markets, where firms often negotiate power purchase agreements (PPAs) years in advance. Galeeva explains that these contracts can extend over a long time—sometimes, 30 to 50 years. There’s little market data for prices and volatilities that far into the future. The new model fills that gap by providing a method to model future volatility when data is limited.
Beyond pricing, the model improves hedging—the practice of using one investment to offset potential losses in another, Galeeva said. When traders hedge a long-term contract with a more liquid short-term contract, neglecting the Samuelson effect may result in erroneous hedging decisions, she says.
“You get a more accurate hedge,” Galeeva explained. “That’s essential in thin or stressed markets.”
The model also provides guidance on when to use a more advanced model—with additional parameters—during periods of extreme market stress, such as during the COVID-19 pandemic or the 2008 financial crisis.
She says it performs significantly better under volatile conditions, offering firms a practical tool for managing risk during uncertainty.