A_R.c: Acceptance-Rejection Algorithm for Constant Objective

In chenqi57/GreenSim: Nested Green Simulation

Description

Simulate random variables from optimal proposal distribution of a constant objective function using Acceptance-Rejection.

Usage

A_R.c(outer, df, rf, N_In = 100)

Arguments

outer	vector of parameters simulated in outer scenario.
df	density functions for the class of distributions inner simulation random variables follow.
rf	random generation for the class of distributions inner simulation random variables follow.
N_In	number of inner replications for each outer scenario.

Value

List of an estimated normalizing constant, a vector of random variables following optimal proposal distribution for constant objective function, and a vector of likelihoods of these random variables.

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
N_In = 5e2      # number of inner 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)
rf <- Curry(rnorm, sd = sig)

A_R.c(mu, df, rf, N_In)

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