Bates_ModelBates Model is a Type that represents the Bates volatility model (1996) whereby the price S of an underlying asset is modelled as a four-factor jump-diffusion process that follows the SDE:
dS = dH + JSdN
H is the Heston process described in Heston Model, albeit with its drift adjusted to compensate for the existence of the jumps.
N is a poisson process with a constant intensity Ξ»
J is a random variable representing the relative jump size Γ„S/S := (S'-S)/S, where S' is the underlying price right after a jump, is distributed in such a way that the logarithm of the "jump factor"S'/S = 1+J is normally distributed.
Formally: log(1+J) ~ N(Ξ½,Ξ΄Β²)
where N(Ξ½,Ξ΄Β²) denotes the standard normal distribution with mean Ξ½ and standard deviation Ξ΄. Web reference available here