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Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised strong interest in recent years, motivated in particular by applications in finance and Internet traffic modelling. Since fBm is not a semi-martingale, stochastic integration requires specific developments. Multifractional...
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We define and study in this work a simple model allowing for a prudential valuation of solvency capital requirement while avoiding over-assessment specifically after market disruption. The main idea is to include a dampener component in charge of refining risk assessment after a market failure....
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Market risk regulations adopted in response to recent crises aim to reduce financial risks. Nevertheless, a large number of practitioners feel that, if these rules seem to succeed in lowering volatility, they appear to rigidify the financial structure of the economic system and tend to increase...
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The generalized multifractional Brownian motion (GMBM) is a continuous Gaussian process that extends the classical fractional Brownian motion (FBM) and multifractional Brownian motion (MBM) (SIAM Rev. 10 (1968) 422; INRIA Res. Rept. 2645 (1995); Rev. Mat. Iberoamericana 13 (1997) 19; Fractals: Theory...
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In this article, we propose several quantization based stratified sampling methods to reduce the variance of a Monte-Carlo simulation. Theoretical aspects of stratification lead to a strong link between the problem of optimal L^2-quantization of a random variable and the variance reduction that...
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This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension...
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