Jump-Diffusion Processes

Jump-diffusion processes are models that combine continuous price movements with sudden, discrete jumps to capture the reality of market shocks. While standard models assume prices follow a smooth path, crypto markets frequently experience abrupt gaps due to news events, liquidity events, or protocol exploits.

These processes use a diffusion component for normal market activity and a jump component to represent significant, unexpected price changes. By accounting for these jumps, models can more accurately price out-of-the-money options and estimate the risk of extreme losses.

This is particularly relevant for crypto derivatives, where tail risk is significantly higher than in traditional asset classes. Jump-diffusion helps in setting appropriate margin requirements and designing robust liquidation triggers.

It bridges the gap between theoretical Gaussian assumptions and the reality of high-volatility financial environments.