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