Deriscope ## The Excel Derivatives Periscope

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Merton76_Model

*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*

where

*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 here