Merton76 Model


Merton76 Model is a direct subtype of Model[Spot Price]
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with functions Merton76 Model Functions, keys Merton76 Model keys and example object Merton76Mdl

TYPE INCLUSION RELATIONSHIPS

Model Spot Price

Merton76 Model

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AVAILABLE FUNCTIONS

Create

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AVAILABLE CREATE FUNCTION KEYS

Discretization

Jump Intensity

Max Iterations

Mean Log Jump Factor

Relative Accuracy

Vol Log Jump Factor

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TYPICAL OBJECTS OF TYPE Merton76 Model

Merton76Mdl

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This type 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