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MonteCarloMethods andAppl., Vol. 11, No. 1, pp. 1 – 14 (2005) c© VSP 2005 An ε-Optimal Portfolio with Stochastic Volatility ∗ Abdelali Gabih and Wilfried Grecksch Martin-Luther-Universitat Halle-Wittenberg, Fachbereich Mathematik und Informatik, Institut für Optimierung und Stochastik, D-06099 Haale (Saale), Germany. E-mails: abdelali.gabih@student.uni-halle.de, grecksch@mathematik.uni-halle.de Abstracts — We consider an extended Merton’s problem of optimal consumption and in- vestment in continuous-time with stochastic volatility. The wealth process of the

introduce the TTLSV model. In Section 3 we detail the EIS-ML method for the parameter estimation of our model. In Section 4 we present a simulation study to examine the accuracy and finite sample properties of the EIS-ML estimates. An empirical analysis on two stock market indices for China is presented in Section 5, and we conclude in Section 6. 2 The triple-threshold leverage stochastic volatility model Let S ( t ) be the asset price at time t and X t be the logarithmic return, defined as X t =ln S ( t )–ln S ( t –1). The classical leverage SV (LSV) model is given

1 Introduction Precise forecasts of asset return volatilities are a centerpiece of many practical applications in financial economics including portfolio allocation, asset pricing and risk assessment. The two most popular approaches for modeling the daily return volatility are GARCH models ( Engle 1982 ; Bollerslev 1986 ) and stochastic volatility (SV) models ( Taylor 1982 , 1986 ). While the volatility itself is not directly observable, GARCH models treat it as measurable given past return observations, while SV models assume that it is an inherently latent

1 Introduction The linear state space model has become a workhorse of macroeconomic and financial time series analysis, not only because it nests a broad set of time series models but also because it allows one to extract useful hidden information out of noisy data. Recently, a class of linear state space models whose disturbances follow stochastic volatility processes (SS-SV model, hereinafter) is increasing in popularity due to the heteroscedastic nature of many economic and financial time series. This paper focuses on the Bayesian Markov-Chain Monte Carlo

Monte Carlo Methods Appl. Vol. 15 No. 4 (2009), pp. 285–310 DOI 10.1515 / MCMA.2009.016 c© de Gruyter 2009 Multiple stochastic volatility extension of the Libor market model and its implementation Denis Belomestny, Stanley Mathew and John Schoenmakers Abstract. In this paper we propose an extension of the Libor market model with a high- dimensional specially structured system of square root volatility processes, and give a road map for its calibration. As such the model is well suited for Monte Carlo simulation of deriva- tive interest rate instruments. As a key

generalizes the usual Box-Jenkins ARIMA model by modelling long term correlation structures as suggested by Mandelbrot and Ness (1968) . The prominence of the ARFIMA model can be seen through various extensions such as the long memory in stochastic volatility process ( Baillie, 1996 ), ARFIMA model with ARCH errors ( Hauser & Kunst, 1998 ) and the fractionally integrated GARCH model with leverage ( Baillie, Bollerslev & Mikkelsen, 1996 ). Although theoretically pleasing, the implementation of the ARFIMA model was a major deterrent. Chan and Palma (1998) operationalized

problems of GAOs since the early 2000s. Ballotta and Haberman (2003) derived the closed-form formula for the GAO price under the one-factor Gaussian Heath–Jarrow–Morton term structure model. See also Pelsser (2003) and Boyle and Hardy (2003) . Biffis and Millossovich (2006) and Chu and Kwok (2007) considered the GAO price under the affine process framework. Recently, van Haastrecht, Plat, and Pelsser (2010) derived the closed-form formula for the GAO price under the stochastic volatility and interest rate model. The authors exploited the Schöbel

1 Introduction The Stochastic Volatility (SV) model, proposed by Taylor (1986) , is one of the basic tools for the analysis of financial time series. In this model, the volatility of the asset is time varying and treated as a latent (unobserved) variable. In the discrete time model introduced by Taylor (1986) , the log-volatility is a first-order autoregressive process, and the basic parameterization of the SV model is given by the following structure: [1] with r t denoting the asset returns in period t, σ t the latent volatility process, the vector of

, such as local volatility model class and stochastic volatility model class. Another stylized fact in the market data is the appearance of jumps in prices. Early jump models have been explored by [ 7 ], in which the jump part is modeled as a compound Poisson process, and the volatility remains constant. Since then, more general models are proposed, for example, stochastic volatility jump model class, which allows jumps appear in both volatility and price process. [ 10 ] described a new radial basis functions (RBFs) algorithm for pricing American options under Merton

Studies in Nonlinear Dynamics & Econometrics Volume 8, Issue 1 2004 Article 1 Private Information andHigh-Frequency Stochastic Volatility David L. Kelly∗ Douglas G.Steigerwald† ∗University of Miami, dkelly@miami.edu †University of California, Santa Barbara, doug@econ.ucsb.edu All rights reserved. Nopart of this publica - tion maybe reproduced,stored in a retrieval system, or transmitted, in anyformor byanymeans, electronic, mechanical, photocopying,recording,or otherwise, without the prior written permis- sion of the publisher, bepress, whichhasbeen given certain