@ARTICLE{16807972_1996,
author = {Bibby, Martin and Sorensen, Michael},
keywords = {finance, model for stock prices, stock market},
title = {Hyperbolic Diffusion Model for Stock Prices},
journal = {Finance and Stochastics},
year = {1996},
month = {},
volume = {1},
number = {},
pages = {25-41},
url = {http://ecsocman.hse.ru/text/16807972/},
publisher = {},
language = {ru},
abstract = {In the present paper we consider a model for stock prices which is a
generalization of the model behind the Black-Scholes formula for
pricing European call options. We model the log-price as a
deterministic linear trend plus a diffusion process with drift zero
and with a diffusion coefficient (volatility) which depends in a
particular way on the instantaneous stock price. It is shown that the
model possesses a number of properties encountered in empirical
studies of stock prices. In particular the distribution of the
adjusted log-price is hyperbolic rather than normal. The model is
rather successfully fitted to two different stock price data sets.
Finally, the question of option pricing based on our model is
discussed and comparison to the Black-Scholes formula is made. The
paper also introduces a simple general way of constructing a
zero-drift diffusion with a given marginal distribution, by which
other models that are potentially useful in mathematical finance can
be developed. },
annote = {In the present paper we consider a model for stock prices which is a
generalization of the model behind the Black-Scholes formula for
pricing European call options. We model the log-price as a
deterministic linear trend plus a diffusion process with drift zero
and with a diffusion coefficient (volatility) which depends in a
particular way on the instantaneous stock price. It is shown that the
model possesses a number of properties encountered in empirical
studies of stock prices. In particular the distribution of the
adjusted log-price is hyperbolic rather than normal. The model is
rather successfully fitted to two different stock price data sets.
Finally, the question of option pricing based on our model is
discussed and comparison to the Black-Scholes formula is made. The
paper also introduces a simple general way of constructing a
zero-drift diffusion with a given marginal distribution, by which
other models that are potentially useful in mathematical finance can
be developed. }
}