AtlasModel: Atlas Model

In RelValAnalysis: Relative Value Analysis

Description

The function AtlasModel is used to create a marketmodel object which represents an Atlas model with user-provided parameters.

Usage

AtlasModel(n, g, sigma)

Arguments

n	a positive integer representing the number of stocks in the market
g	a positive number. In this model, n*g is the growth rate of the smallest stock.
sigma	a positive number representing the common volatility of the stocks.

Details

The definition of the Atlas model follows Example 5.3.3 in Fernholz (2002). The stochastic differential equation of the market capitalizations X_i(t) for the i-th stock takes the form

dlog X_i(t) = gamma_i(t)dt + sigma dW_i(t), i = 1, ..., n,

where gamma_i(t) = ng if stock i is the smallest, and is 0 otherwise.

It is the simplest market model which exhibits an asymptotic Pareto-shaped capital distribution curve.

Value

A marketmodel object.

References

Fernholz, E. R. (2002) Stochastic portfolio theory. Springer.

See Also

marketmodel, SimMarketModel

Examples

# Create an Atlas model of 100 stocks
model <- AtlasModel(n = 100, g = 0.001, sigma = 0.2)

# Simulate the Atlas model to get 5 years of monthly data
market <- SimMarketModel(model, n.years = 5, frequency = 12)

Example output

Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

RelValAnalysis documentation built on May 2, 2019, 3:09 a.m.