scholarly journals Markov Regime Switching of Stochastic Volatility Lévy Model on Approximation Mode

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Arthit Intarasit
Keyword(s):  
Stochastic Volatility ◽  
Regime Switching ◽  
Lévy Process ◽  
Stock Exchange ◽  
Asset Returns ◽  
Levy Process ◽  
Martingale Measure ◽  
Large Set ◽  
Proposed Model ◽  
Risk Neutral

This paper deals with financial modeling to describe the behavior of asset returns, through consideration of economic cycles together with the stylized empirical features of asset returns such as fat tails. We propose that asset returns are modeled by a stochastic volatility Lévy process incorporating a regime switching model. Based on the risk-neutral approach, there exists a large set of candidates of martingale measures due to the driving of a stochastic volatility Lévy process in the proposed model which renders the market incomplete in general. We first establish an equivalent martingale measure for the proposed model introduced in risk-neutral version. Regime switching of stochastic volatility Lévy process is employed in an approximation mode for model calibration and the calibration of parameters model done based on EM algorithm. Finally, some empirical results are illustrated via applications to the Bangkok Stock Exchange of Thailand index.

scholarly journals A fuzzy approach to option pricing in a Levy process setting

2013 ◽  
Vol 23 (3) ◽  
pp. 613-622 ◽  
Author(s):  
Piotr Nowak ◽  
Maciej Romaniuk
Keyword(s):  
Option Pricing ◽  
Lévy Process ◽  
Fuzzy Numbers ◽  
Levy Process ◽  
Martingale Measure ◽  
Fuzzy Arithmetic ◽  
European Option ◽  
European Call Option ◽  
Log Price ◽  
Geometric Levy Process

Abstract In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets.We assume that some parameters of the financial instrument cannot be precisely described and therefore they are introduced to the model as fuzzy numbers. Application of fuzzy arithmetic enables us to consider various sources of uncertainty, not only the stochastic one. To obtain the European call option pricing formula we use the minimal entropy martingale measure and Levy characteristics.

scholarly journals Detection of Patches of Outliers in Stochastic Volatility Processes

2014 ◽  
Vol 8 (2) ◽  
pp. 169
Author(s):  
Anderson C.O. Motta ◽  
Luiz K. Hotta
Keyword(s):  
New York ◽  
Stochastic Volatility ◽  
Stock Exchange ◽  
Statistical Tests ◽  
Asset Returns ◽  
Sampling Procedure ◽  
New York Stock Exchange ◽  
Simulated Sample ◽  
York Stock Exchange ◽  
Daily Returns

Because the volatility of nancial asset returns tends to arrive in clusters, it is quite likely that outliers appear in patches. In this case, most of the statistical tests developed to detect outliers have low power. We propose to use the posterior distribution of the size of the outlier and of the probability of the presence of an outlier at each observation to detect and estimate the outlier. This sampling algorithm is an adapted version of the algorithm proposed by Justel et al. (2001) for autoregressive time-series models. Our proposed sampling procedure is applied to a simulated sample according to the stochastic volatility, a sample of the New York Stock Exchange daily returns, and a sample of the Brazilian S~ao Paulo Stock Exchange daily returns.

Option pricing and hedging under a stochastic volatility Lévy process model

2011 ◽  
Vol 15 (1) ◽  
pp. 81-97 ◽  
Author(s):  
Young Shin Kim ◽  
Frank J. Fabozzi ◽  
Zuodong Lin ◽  
Svetlozar T. Rachev
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Lévy Process ◽  
Process Model ◽  
Levy Process

scholarly journals Portfolio Strategy of Financial Market with Regime Switching Driven by Geometric Lévy Process

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Liuwei Zhou ◽  
Zhijie Wang
Keyword(s):  
Financial Market ◽  
Stock Prices ◽  
Regime Switching ◽  
Lévy Process ◽  
Parabolic Type ◽  
Levy Process ◽  
Portfolio Strategy ◽  
Set Up ◽  
S Model ◽  
Geometric Levy Process

The problem of a portfolio strategy for financial market with regime switching driven by geometric Lévy process is investigated in this paper. The considered financial market includes one bond and multiple stocks which has few researches up to now. A new and general Black-Scholes (B-S) model is set up, in which the interest rate of the bond, the rate of return, and the volatility of the stocks vary as the market states switching and the stock prices are driven by geometric Lévy process. For the general B-S model of the financial market, a portfolio strategy which is determined by a partial differential equation (PDE) of parabolic type is given by using Itô formula. The PDE is an extension of existing result. The solvability of the PDE is researched by making use of variables transformation. An application of the solvability of the PDE on the European options with the final data is given finally.

scholarly journals A Bayesian Semiparametric Realized Stochastic Volatility Model

2021 ◽  
Vol 14 (12) ◽  
pp. 617
Author(s):  
Jia Liu
Keyword(s):  
Stochastic Volatility ◽  
Asset Returns ◽  
Realized Volatility ◽  
Stochastic Volatility Model ◽  
Estimation Bias ◽  
Bayesian Nonparametric ◽  
Proposed Model ◽  
Volatility Model ◽  
Flexible Framework ◽  
Density Forecasts

This paper proposes a semiparametric realized stochastic volatility model by integrating the parametric stochastic volatility model utilizing realized volatility information and the Bayesian nonparametric framework. The flexible framework offered by Bayesian nonparametric mixtures not only improves the fitting of asymmetric and leptokurtic densities of asset returns and logarithmic realized volatility but also enables flexible adjustments for estimation bias in realized volatility. Applications to equity data show that the proposed model offers superior density forecasts for returns and improved estimates of parameters and latent volatility compared with existing alternatives.

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