jumpdiffusion
Jump diffusion is a class of stochastic processes used to model quantities that evolve with both continuous fluctuations and sudden, discrete changes. It extends a pure diffusion model by incorporating jumps, allowing for abrupt moves in value that occur at random times.
A common formulation for a jump-diffusion process S_t is given by the stochastic differential equation dS_t =
A common variant is the Merton jump-diffusion model, where jump sizes are multiplicative with J = e^Y
Applications of jump diffusion appear in options pricing, risk management, and credit or energy markets, where