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  • 2000-2004  (4)
  • 2001  (4)
  • PACS. 05.45.Tp Time series analysis – 02.50.Ey Stochastic processes  (2)
  • PACS. 64.60.-i General studies of phase transitions – 64.60.Fr Equilibrium properties near critical points, critical exponents – 75.40.-s Critical-point effects, specific heats, short-range order  (2)
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  • 2000-2004  (4)
Year
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  • 1
    Electronic Resource
    Electronic Resource
    Beliefs and stochastic modelling of interest rate scenario risk (2001)
    Springer
    The European physical journal 20 (2001), S. 511-515 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 05.45.Tp Time series analysis – 02.50.Ey Stochastic processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: We present a framework that allows for a systematic assessment of risk given a specific model and belief on the market. Within this framework the time evolution of risk is modeled in a twofold way. On the one hand, risk is modeled by the time discrete and nonlinear garch(1,1) process, which allows for a (time-)local understanding of its level, together with a short term forecast. On the other hand, via a diffusion approximation, the time evolution of the probability density of risk is modeled by a Fokker-Planck equation. Then, as a final step, using Bayes theorem, beliefs are conditioned on the stationary probability density function as obtained from the Fokker-Planck equation. We believe this to be a highly rigorous framework to integrate subjective judgments of future market behavior and underlying models. In order to demonstrate the approach, we apply it to risk assessment of empirical interest rate scenario methodologies, i.e. the application of Principal Component Analysis to the the dynamics of bonds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00011107
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Extracting factors for interest rate scenarios (2001)
    Springer
    The European physical journal 20 (2001), S. 517-522 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 05.45.Tp Time series analysis – 02.50.Ey Stochastic processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: Factor based interest rate models are widely used for risk managing purposes, for option pricing and for identifying and capturing yield curve anomalies. The movements of a term structure of interest rates are commonly assumed to be driven by a small number of orthogonal factors such as SHIFT, TWIST and BUTTERFLY (BOW). These factors are usually obtained by a Principal Component Analysis (PCA) of historical bond prices (interest rates). Although PCA diagonalizes the covariance matrix of either the interest rates or the interest rate changes, it does not use both covariance matrices simultaneously. Furthermore higher linear and nonlinear correlations are neglected. These correlations as well as the mean reverting properties of the interest rates become crucial, if one is interested in a longer time horizon (infrequent hedging or trading). We will show that Independent Component Analysis (ICA) is a more appropriate tool than PCA, since ICA uses the covariance matrix of the interest rates as well as the covariance matrix of the interest rate changes simultaneously. Additionally higher linear and nonlinear correlations may be easily incorporated. The resulting factors are uncorrelated for various time delays, approximately independent but nonorthogonal. This is in contrast to the factors obtained from the PCA, which are orthogonal and uncorrelated for identical times only. Although factors from the ICA are nonorthogonal, it is sufficient to consider only a few factors in order to explain most of the variation in the original data. Finally we will present examples that ICA based hedges outperforms PCA based hedges specifically if the portfolio is sensitive to structural changes of the yield curve.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Subleading long-range interactions and violations of finite size scaling (2001)
    Springer
    The European physical journal 21 (2001), S. 251-268 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 64.60.-i General studies of phase transitions – 64.60.Fr Equilibrium properties near critical points, critical exponents – 75.40.-s Critical-point effects, specific heats, short-range order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor system. In the context of the mean spherical model with periodic boundary conditions we are able to identify, for temperatures close above T c, finite-size contributions due to the subleading term in the interaction that are dominant in this region decaying algebraically as a function of L. This mechanism goes beyond the standard formulation of the finite-size scaling but is to be expected in real physical systems. We also discuss other ways in which critical point behavior is modified that are of relevance for analysis of Monte Carlo simulations of such systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s100510170201
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Two-point correlation function in systems with van der Waals type interaction (2001)
    Springer
    The European physical journal 23 (2001), S. 211-219 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 64.60.-i General studies of phase transitions – 64.60.Fr Equilibrium properties near critical points, critical exponents – 75.40.-s Critical-point effects, specific heats, short-range order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: The behavior of the bulk two-point correlation function G( ;T| d ) in d-dimensional system with van der Waals type interactions is investigated and its consequences on the finite-size scaling properties of the susceptibility in such finite systems with periodic boundary conditions is discussed within mean-spherical model which is an example of Ornstein and Zernike type theory. The interaction is supposed to decay at large distances r as r - (d + σ), with 2 〈 d 〈 4, 2 〈 σ 〈 4 and d + σ≤6. It is shown that G( ;T| d ) decays as r - (d - 2) for 1 ≪r≪ξ, exponentially for ξ≪r≪r *, where r * = (σ - 2)ξlnξ, and again in a power law as r - (d + σ) for r≫r *. The analytical form of the leading-order scaling function of G( ;T| d ) in any of these regimes is derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s100510170070
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    Paper (German National Licenses)
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