{"id":53980,"date":"2025-09-16T13:12:31","date_gmt":"2025-09-16T17:12:31","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=news&p=53980"},"modified":"2025-09-17T13:33:00","modified_gmt":"2025-09-17T17:33:00","slug":"meet-the-math-that-puts-known-commodity-behavior-to-work-in-more-accurate-derivatives-pricing","status":"publish","type":"news","link":"https:\/\/engineering.jhu.edu\/ams\/news\/meet-the-math-that-puts-known-commodity-behavior-to-work-in-more-accurate-derivatives-pricing\/","title":{"rendered":"Meet the math that puts known commodity behavior to work in more accurate derivatives pricing\u00a0"},"content":{"rendered":"

Traders and energy companies <\/span>risk costly mistakes when pricing commodity derivatives\u2014financial contracts tied to oil, gas, and other commodities\u2014if they overlook a market phenomenon known as the Samuelson effect, according to new research by a Johns Hopkins mathematician. Published in <\/span>the <\/span>Multidisciplinary Digital Publishing Institute (MDPI)<\/span><\/i><\/a> journal,<\/span> 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.<\/span>\u00a0<\/span><\/p>\n

Roza Galeeva<\/span><\/a>, senior lecturer in the Whiting School of Engineering\u2019s <\/span>Department of Applied Mathematics and Statistics<\/span><\/a>, 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.<\/span>\u00a0<\/span><\/p>\n

\u201cPeople sometimes try to use the same models they use for stocks,\u201d said Galeeva. \u201cBut commodities behave differently\u2013you\u2019re dealing with real physical goods, not just paper assets.\u201d<\/span>\u00a0<\/span><\/p>\n

Her research, developed through years of academic and industry work\u2014including projects with graduate students at NYU and later at Johns Hopkins\u2014proposes 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\u2014an especially important factor for pricing path-dependent options.<\/span>\u00a0<\/span><\/p>\n

\u201cThink of variance as a clock,\u201d she said. \u201cAt the start of a contract, time moves slowly. But as you get closer to expiration, things speed up. That\u2019s how variance behaves\u2014and that is how, through modeling of a clock with exponential decay, we capture the phenomenon.\u201d<\/span>\u00a0<\/span><\/p>\n

Galeeva\u2019s approach relies on historical market data and can be efficiently calibrated, making it useful for practitioners who need fast, accurate pricing tools.<\/span>\u00a0<\/span>\u00a0<\/span><\/p>\n

She tested the model using this data and ran it through a robust calibration process, using statistical tests\u2014similar to machine learning techniques\u2014to confirm its accuracy. Testing revealed that the model delivered dependable results within industry standards.\u202f\u202f\u202f<\/span>\u00a0<\/span><\/p>\n

\u201cThis isn\u2019t just theoretical. We tested it with historical data,\u201d said Galeeva. \u201cIt holds up\u2014and it’s easy to update as markets evolve.\u201d\u202f<\/span>\u00a0<\/span><\/p>\n

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\u2014sometimes, 30 to 50 years. There\u2019s 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.\u202f<\/span>\u00a0<\/span><\/p>\n

Beyond pricing, the model improves hedging\u2014the 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.<\/span>\u00a0<\/span>\u202f<\/span>\u00a0<\/span><\/p>\n

\u201cYou get a more accurate hedge,\u201d Galeeva explained. \u201cThat\u2019s essential in thin or stressed markets.\u201d\u202f<\/span>\u00a0<\/span><\/p>\n

\u202f<\/span>The model also provides guidance on when to use a more advanced model\u2014with additional parameters\u2014during periods of extreme market stress, such as during the COVID-19 pandemic or the 2008 financial crisis.<\/span>\u00a0<\/span><\/p>\n

She says it performs significantly better under volatile conditions, offering firms a practical tool for managing risk during uncertainty.\u202f<\/span>\u00a0<\/span><\/p>\n","protected":false},"template":"","class_list":["post-53980","news","type-news","status-publish","hentry","news_categories-financial-mathematics","news_categories-research"],"acf":[],"yoast_head":"\nMeet the math that puts known commodity behavior to work in more accurate derivatives pricing\u00a0 | Department of Applied Mathematics and Statistics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/engineering.jhu.edu\/ams\/news\/meet-the-math-that-puts-known-commodity-behavior-to-work-in-more-accurate-derivatives-pricing\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Meet the math that puts known 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