Deriscope ## The Excel Derivatives Periscope

##### Coverage

Bates_Model

*Bates Model* is a child type of Model[Spot Price] 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*

where

*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