VolStabModel: Volatility-Stabilized Model

In RelValAnalysis: Relative Value Analysis

Description

The function VolStabModel is used to create a marketmodel object which represents an volatility-stabilized market model with user-provided parameters.

Usage

VolStabModel(n, alpha, sigma)

Arguments

n	a positive integer representing the number of stocks in the market.
alpha	a non-negative number. It is a growth rate parameter.
sigma	a positive number. It is a volatility parameter.

Details

The definition of the volatility-stabilized model is taken from Section 12 of Fernholz and Karatzas (2009). The stochastic differential equation of the market capitalization X_i(t) of the i-th stock takes the form

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

where

gamma_i(t) = alpha / 2mu_i(t)

and

sigma_i(t) = 1 / sqrt(mu_i(t)).

This is a model which captures the idea that smaller stocks have larger growth rates and are more volatile.

Value

A marketmodel object.

References

Karatzas, I. and R. Fernholz (2009). Stochastic portfolio theory: an overview. Handbook of numerical analysis 15, 89-167.

See Also

marketmodel, SimMarketModel

Examples

# Create a Volatility stabilized market of 10 stocks
model <- VolStabModel(n = 10, alpha = 0.1, sigma = 0.1)

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.