BaPreStoPro (version 0.1)

Merton-class: S4 class of model informations for a special jump diffusion process, called Merton model

Description

Informations of model $dY_t = \phi Y_t dt + \gamma^2 Y_t dW_t + \theta Y_tdN_t$ with $N_t\sim Pois(\Lambda(t, \xi))$. The explicit solution of the SDE is given by $Y_t = y_0 \exp( \phi t - \gamma^2/2 t+\gamma W_t + \log(1+\theta) N_t)$.

Slots

thetaT

parameter $\widetilde{\theta}=\log(1+\theta)$

phi

parameter $\phi$

gamma2

parameter $\gamma^2$

xi

parameter $\xi$

Lambda

function $\Lambda(t,\xi)$

prior

list of prior parameters for $\phi, \widetilde{\theta}, \gamma^2$

priorDensity

list of prior density function for $\xi$

start

list of starting values for the Metropolis within Gibbs sampler

Examples

parameter <- list(phi = 0.01, thetaT = 0.1, gamma2 = 0.01, xi = c(2, 0.2))
Lambda <- function(t, xi) (t / xi[2])^xi[1]
# prior density for xi:
priorDensity <- function(xi) dgamma(xi, c(2, 0.2), 1)
# prior parameter for phi (normal), thetaT (normal) and gamma2 (inverse gamma):
prior <- list(m.phi = parameter$phi, v.phi = parameter$phi, m.thetaT = parameter$thetaT,
   v.thetaT = parameter$thetaT, alpha.gamma = 3, beta.gamma = parameter$gamma2*2)
start <- parameter
model <- set.to.class("Merton", parameter, prior, start, Lambda = Lambda,
   priorDensity = priorDensity)
summary(class.to.list(model))
# default:
model <- set.to.class("Merton", parameter, Lambda = Lambda)