g.star: Optimal Proposal Distribution

In chenqi57/GreenSim: Nested Green Simulation

Description

Calculate the density of optimal proposal distribution without normalizing constant for the specified objective function.

Usage

g.star(x, outer, df, h)

Arguments

x	vector of random variables.
outer	vector of parameters simulated in outer scenario.
df	density functions for the class of distributions inner simulation random variables follow.
h	objective function.

Value

Density without normalizing constant of the input random variable vector.

Examples

library(functional)
r = 5e-2    # risk-free rate
S0 = 100    # initial stock price
vol = 30e-2 # annual volatility

tau = 1/12    # one month
T = 1         # time to maturity (from time 0)

N_Out = 10     # number of outer samples

T2M = T - tau

min <- qlnorm(1e-4, meanlog = (r-0.5*vol^2)*tau + log(S0), sdlog = (vol*sqrt(tau)))
max <- qlnorm(1-1e-4, meanlog = (r-0.5*vol^2)*tau + log(S0), sdlog = (vol*sqrt(tau)))
S_tau <- seq(from = min, to = max, length.out = N_Out)
mu <- log(S_tau) + (r-0.5*vol^2)*T2M
sig <- vol * sqrt(T2M)
df <- Curry(dnorm, sd = sig)

x <- seq(from = 4, to = 6, length.out = 10)
h <- function(x){return(pmax(exp(x)-90, 0))}

g.star(x, mu, df, h)

chenqi57/GreenSim documentation built on Dec. 19, 2021, 3:04 p.m.