# First Exit-Time Analysis for an Approximate Barndorff-Nielsen and Shephard Model with Stationary Self-Decomposable Variance Process

@article{Awasthi2021FirstEA, title={First Exit-Time Analysis for an Approximate Barndorff-Nielsen and Shephard Model with Stationary Self-Decomposable Variance Process}, author={Shantanu Awasthi and Indranil Sengupta}, journal={Journal of Stochastic Analysis}, year={2021} }

In this paper, an approximate version of the Barndorff-Nielsen and Shephard model, driven by a Brownian motion and a L\'evy subordinator, is formulated. The first-exit time of the log-return process for this model is analyzed. It is shown that with certain probability, the first-exit time process of the log-return is decomposable into the sum of the first exit time of the Brownian motion with drift, and the first exit time of a L\'evy subordinator with drift. Subsequently, the probability…

## 4 Citations

Alòs Type Decomposition Formula for Barndorff-Nielsen and Shephard Model

- MathematicsJournal of Stochastic Analysis
- 2020

The objective is to provide an Al\`os type decomposition formula of call option prices for the Barndorff-Nielsen and Shephard model: an Ornstein-Uhlenbeck type stochastic volatility model driven by a…

Analysis of stock index with a generalized BN-S model: an approach based on machine learning and fuzzy parameters

- Computer ScienceStochastic Analysis and Applications
- 2022

The results show that the new model, where fuzzy parameters are incorporated, can incorporate the long-term dependence in the classical Barndorff-Nielsen and Shephard model and effectively captures the stochastic dynamics of stock index time series.

Generalized BN-S Model Application: Analysis of Stock Index Option Price Volatility Based on Machine Learning and Fuzzy Parameters

- Computer Science
- 2021

The results show that the new model in a fuzzy environment solves the long-term dependence problem of the classic model with fewer parameter changes, and effectively analyzes the random dynamic characteristics of stock index option price time series.

Modeling dynamic volatility under uncertain environment with fuzziness and randomness

- Economics
- 2022

: Predicting the dynamic volatility in ﬁnancial market provides a promising method for risk prediction, asset pricing and market supervision. Barndorﬀ-Nielsen and Shephard model (BN-S) model, used to…

## References

SHOWING 1-10 OF 58 REFERENCES

First-exit times of an inverse Gaussian process

- Mathematics
- 2011

Abstract The first-exit time process of an inverse Gaussian Lévy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and…

Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes

- Mathematics
- 2009

Numerical Computation of First-Passage Times of Increasing Lévy Processes

- Mathematics
- 2009

Let {D(s), s ≥ 0} be a non-decreasing Lévy process. The first-hitting time process {E(t), t ≥ 0} (which is sometimes referred to as an inverse subordinator) defined by $E(t) = \inf \{s: D(s) > t \}$…

First and Last Passage Times of Spectrally Positive Lévy Processes with Application to Reliability

- Mathematics
- 2015

We consider a wide class of increasing Lévy processes perturbed by an independent Brownian motion as a degradation model. Such family contains almost all classical degradation models considered in…

The first exit time of Brownian motion from a parabolic domain

- Mathematics
- 2002

Consider a planar Brownian motion starting at an interior point of the parabolic domain D = {(x, y) :y > x2}, and let TrD denote the first time the Brownian motion exits from D. The tail behaviour…

The First Exit Time Stochastic Theory Applied to Estimate the Life-Time of a Complicated System

- MathematicsMethodology and Computing in Applied Probability
- 2019

We develop a first exit time methodology to model the life time process of a complicated system. We assume that the functionality level of a complicated system follows a stochastic process during…

First passage times of diffusion processes and their applications to finance

- Economics
- 2019

The purpose of this thesis is to provide quantitative tools for investment decision and risk management by combining probability theory with financial practice, and to solve the closed-form asymptotic for the model’s first passage time.

Some remarks on first passage of Levy processes, the American put and pasting principles

- Mathematics
- 2005

The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed…