Go to Deriscope's documentation start page


Merton76 Model is a Type that represents the Merton jump-diffusion model (1976) whereby the price S of an underlying asset is modelled as a three-factor jump-diffusion process that follows the SDE:
dS = (α-λk)Sdt + σSdB + JSdN
α = the asset's risk-free rate of return
N is a
poisson process with a constant intensity λ
B is a Brownian motion
σ = constant interpreted as the volatility of the non-jump part of the process
J is a random variable representing the relative jump size ΔS/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(μ,δ²)
where N(μ,δ²) denotes the standard normal distribution with mean μ and standard deviation δ. Web reference available