ls.fitting: Least Square Fitting for Optimal Beta for Optimal Proposal...

In chenqi57/GreenSim: Nested Green Simulation

Description

Fit optimal weights of each outer scenario distibution by Least Square, aiming to mimic optimal proposal distibution of the specified objective function by a mixture distribution.

Usage

ls.fitting(outer, df, rf, N_In = 100, h)

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.

Value

List of both a vector of optimal weights of each outer scenario distibution and a vector of MLR random variables used in fitting these weights.

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)}

ls.fitting(mu, df, rf, N_In, h)

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