NGS_OIS: Optimal Importance Sampling Estimators

In chenqi57/GreenSim: Nested Green Simulation

Description

Calculate Optimal Importance Sampling estimators of the specified bounded objective function at each outer scenario from nested Green Simulation.

Usage

NGS_OIS(outer, df, rf, N_In = 100, h, M, sn = FALSE)

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.
h	objective function.
M	upper bound of objective function's absolute value.
sn	logical; if TRUE, self-normalized the likelihood ratios.

Value

A vector of Optimal Importance Sampling estimates for each outer scenario. The length of the result is determined by number of outer scenarios.

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)

h <- function(x){return(pmax(exp(x)-90, 0) - pmax(exp(x)-110, 0) + 10)}
M <- 30

NGS_OIS(mu, df, rf, N_In, h, M, TRUE)
NGS_OIS(mu, df, rf, N_In, h, M, FALSE)

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