Abstract
The aim of this paper is to study the tail distribution of the CEV model driven by Brownian motion and fractional Brownian motion. Based on the techniques of Malliavin calculus and a result established recently in [<a href="#1">1</a>], we obtain an explicit estimate for tail distributions.
Highlights
I t is well known that the CEV model is one of very popular models in finance
The aim of this paper is to study the tail distribution of the CEV model driven by Brownian motion and fractional Brownian motion
T is well known that the CEV model is one of very popular models in finance. The dynamic of this model is described by the following Itô stochastic differential equation t t
Summary
I t is well known that the CEV model is one of very popular models in finance The dynamic of this model is described by the following Itô stochastic differential equation t t. We recall that a fractional Brownian motion (fBm) of Hurst parameter H ∈ (0, 1) is a centered Gaussian process BH = (BtH)0≤t≤T with covariance function. We consider the mixed-fractional CEV model that is defined as the stochastic differential equations of the form t t t. Our aim is to study the tail distribution of solutions to (3) This problem is important because the probability distribution function is one of the most natural features for any random variable. The volatility coefficient of the model (3) violates the Lipschitz continuous condition which is traditionally imposed in the study of stochastic differential equations.
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