{"id":61547,"date":"2026-09-03T17:03:36","date_gmt":"2026-09-03T09:03:36","guid":{"rendered":"https:\/\/www.vtmarkets.com\/en-asia\/uncategorized\/jump-diffusion-definition\/"},"modified":"2026-09-03T17:03:36","modified_gmt":"2026-09-03T09:03:36","slug":"jump-diffusion-definition","status":"publish","type":"post","link":"https:\/\/www.vtmarkets.com\/en-asia\/trading-glossary\/jump-diffusion-definition\/","title":{"rendered":"Jump diffusion Definition"},"content":{"rendered":"

What Is Jump Diffusion and How Does It Model Price Behaviour?<\/h2>\n

Jump diffusion is a class of financial model that describes asset price movements as a combination of two processes: a continuous diffusion component \u2014 the gradual, random price fluctuations that occur over time \u2014 and a discontinuous jump component that accounts for sudden, large price moves. These jumps represent the kind of abrupt market shifts triggered by unexpected events such as earnings shocks, policy announcements, geopolitical incidents, or liquidity crises.<\/p>\n

Continuous vs. Discontinuous Price Movement<\/h3>\n\n\n\n\n\n\n\n\n
Feature<\/strong><\/th>\nContinuous (Diffusion)<\/strong><\/th>\nDiscontinuous (Jump)<\/strong><\/th>\n<\/tr>\n<\/thead>\n
Nature of movement<\/td>\nGradual, incremental changes<\/td>\nSudden, large discrete moves<\/td>\n<\/tr>\n
Cause<\/td>\nDay-to-day market noise and flow<\/td>\nNews events, crises, announcements<\/td>\n<\/tr>\n
Modelled by<\/td>\nBrownian motion (Wiener process)<\/td>\nPoisson process with random magnitude<\/td>\n<\/tr>\n
Frequency<\/td>\nConstant<\/td>\nRandom, relatively rare<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

How the Jump Diffusion Model Works<\/h2>\n

The most widely referenced jump diffusion model is the Merton (1976) framework, which combines a geometric Brownian motion for continuous price drift with a compound Poisson process that introduces random jumps of random magnitude at random times. The model requires three additional parameters beyond standard diffusion: the expected number of jumps per year (jump intensity), the average jump size, and the volatility of jump sizes.<\/p>\n

Jump Diffusion vs. the Black-Scholes Model<\/h2>\n

The standard Black-Scholes options pricing model assumes that asset prices follow a continuous path with constant volatility \u2014 an assumption that fails to account for the observed ‘fat tails’ and volatility smiles in real options markets. Jump diffusion models improve on this by explicitly modelling the probability of sudden large moves, producing option prices that better reflect the market’s observed pricing of deep out-of-the-money options and short-dated contracts where jump risk is most significant.<\/p>\n

Applications in Finance<\/h2>\n

Jump diffusion models are applied across several areas of financial practice:<\/p>\n