Wolfgang Schadner
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Schadner
First name
Wolfgang
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wolfgang.schadner@unisg.ch
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+41 71 224 70 08

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  • Publication
    Estimating Forward-Looking Stock Correlations from Risk Factors
    ( 2022-05-12)
    Wolfgang Schadner
    ;
    Joshua Traut orcid-logo
    This study provides fully mathematically and economically feasible solutions to estimating implied correlation matrices in equity markets. Factor analysis is combined with option data to receive ex ante beliefs for cross-sectional correlations. Necessary conditions for implied correlation matrices to be realistic, both in a mathematical and in an economical sense, are developed. An evaluation of existing models reveals that none can comply with the developed conditions consistently. This study overcomes this pitfall and provides two estimation models via exploiting the underlying factor structure of returns. The first solution reformulates the task into a constrained nearest correlation matrix problem. This method can be used either as a stand-alone instrument or as a repair tool to re-establish the feasibility of another model’s estimate. One of these properties is matrix invertibility, which is especially valuable for portfolio optimization tasks. The second solution transforms common risk factors into an implied correlation matrix. The solutions are evaluated upon empirical experiments of S&P 100 and S&P 500 data. They turn out to require modest computational power and comply with the developed constraints. Thus, they provide practitioners with a reliable method to estimate realistic implied correlation matrices.
    Type: journal article
    Journal: Mathematics
    Volume: 10
    Issue: 10
    DOI: 10.3390/math10101649
    URI: https://www.alexandria.unisg.ch/handle/20.500.14171/118171
  • Publication
    Which is Worse: Heavy Tails or Volatility Clusters?
    ( 2023-06-15)
    Joshua Traut orcid-logo
    ;
    Wolfgang Schadner
    Heavy tails and volatility clusters are both stylized facts of financial returns that destabilize markets. The former are extreme events by definition and the latter can accelerate adverse market developments. This work disentangles the two sources and examines which one does the greater damage to financial stability, whether the threat can be reduced via diversification, and how an acknowledgment of volatility clustering can enhance the quality of risk models. The analysis is carried out for index return series representing seven different asset classes and for individual stock portfolio return series. The isolation of the stylized facts is achieved under recent developments in surrogate analysis (IAAFT, IAAWT). While tail risk historically received more attention, especially in financial regulation, our analysis shows that volatility clusters have a greater impact on maximum drawdowns and aggregate losses across all return series. We further find that diversification does not yield any protection from those risks. These findings have important implications for financial regulators, risk managers, and investors seeking to understand and mitigate the risks of financial markets.
    Type: conference paper
    DOI: 10.2139/ssrn.4410908
    URI: https://www.alexandria.unisg.ch/handle/20.500.14171/117505
  • Publication
    Direct Fit for SVI Implied Volatilities
    ( 2023-07-07)
    Schadner, Wolfgang
    The stochastic volatility inspired (SVI) formula is one of the mainstream models for fitting the option implied volatility smile. Herein I fully linearize the SVI equation by rewriting it into the algebraic form of a conic section, limited to the geometric shape of a hyperbola. This step reduces the complexity of the otherwise non-linear optimization problem significantly. Based on the conic representation, I introduce the direct least-squares for SVI, allowing us to fit the model in a computationally efficient and non-iterative manner. The performance of the proposed method is evaluated upon empirical data of seven different asset classes. It turns out to deliver a very good fit, and is about 25 times faster than the existing 'quasi-explicit' benchmark algorithm. Following the outstanding computational speed combined with the high accuracy, the direct SVI fit qualifies as a robust method for calibrating implied volatilities in real-time, and for applications to big option datasets.
    Type: working paper
    URI: https://www.alexandria.unisg.ch/handle/20.500.14171/117638
  • Project
    Direct Fit for SVI Implied Volatilities
    ( 2023-07-07)
    Schadner, Wolfgang
    The stochastic volatility inspired (SVI) formula is one of the mainstream models for fitting the option implied volatility smile. It is traditionally calibrated using multi-parameter non-linear optimization routines. In contrast, in this study I reveal that the SVI equation represents a conic section, limited to the geometric shape of a hyperbola. This insight enables a full linearization of the SVI formula, making the fitting task significantly simpler. By using the linearized equation, we can fit the empirical data directly with a non-iterative and type-specific least-squares method, resulting in a computational efficient and numerical stable closed-form solution. To prove the effectiveness of this approach, I conduct calibration experiments on empirical data of various asset classes, demonstrating the robustness and accuracy of the method.