Merton-class: S4 class of model informations for a special jump diffusion...

In BaPreStoPro: Bayesian Prediction of Stochastic Processes

Description

Informations of model dY_t = φ Y_t dt + γ^2 Y_t dW_t + θ Y_tdN_t with N_t\sim Pois(Λ(t, ξ)). The explicit solution of the SDE is given by Y_t = y_0 \exp( φ t - γ^2/2 t+γ W_t + \log(1+θ) N_t).

Slots

thetaT

parameter \widetilde{θ}=\log(1+θ)

phi

parameter φ

gamma2

parameter γ^2

xi

parameter ξ

Lambda

function Λ(t,ξ)

prior

list of prior parameters for φ, \widetilde{θ}, γ^2

priorDensity

list of prior density function for ξ

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)

Example output

             Length Class  Mode    
thetaT       1      -none- numeric 
phi          1      -none- numeric 
gamma2       1      -none- numeric 
xi           2      -none- numeric 
Lambda       1      -none- function
prior        6      -none- list    
start        4      -none- list    
priorDensity 1      -none- function

BaPreStoPro documentation built on May 2, 2019, 3:34 p.m.