On the complete model with stochastic volatility by Hobson and Rogers
نویسندگان
چکیده
منابع مشابه
On the complete model with stochastic volatility by Hobson and Rogers
In the complete model with stochastic volatility by Hobson and Rogers, preference independent options prices are solutions to degenerate partial differential equations obtained by including additional state variables describing the dependence on past prices of the underlying. In this paper, we aim to emphasize the mathematical tractability of the model by presenting analytical and numerical res...
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Monte Carlo estimators of sensitivity indices and the marginal density of the price dynamics are derived for the Hobson-Rogers stochastic volatility model. Our approach is based mainly upon the Kolmogorov backward equation by making full use of the Markovian property of the dynamics given the past information. Some numerical examples are presented with a GARCHlike volatility function and its ex...
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In this paper, we take the model of Hobson & Rogers (1998) for the movement of an asset, and we fit it to data. The model of Hobson & Rogers is a stochastic volatility model, where the volatility depends on the offset of the current log-price from its exponentially-weighted historical value. As such, the model is complete, and there are unique preference-independent prices. In the datasets we s...
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The path-dependent volatility model by Hobson and Rogers is considered. It is known that this model can potentially reproduce the observed smile and skew patterns of different directions, while preserving the completeness of the market. In order to quantitatively investigate the pricing performance of the model a calibration procedure is here derived. Numerical results based on S&P500 option pr...
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The paper proposes an original class of models for the continuous time price process of a nancial security with non-constant volatility. The idea is to deene instantaneous volatility in terms of exponentially-weighted moments of historic log-price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that unlike many other models of non-consta...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2004
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2004.1370