• Implied Volatility: An old problem with a new solution.

    • Speaker: Kathrin Glau| Lecturer in Financial Mathematics at Queen Mary University of London
    • Date: 12th June 2018 – 18:30
      Place: Thomson Reuters, 30 South Colonnade, Canary Wharf E14 5EP
    • Topic: Implied Volatility: An old problem with a new solution.

    The implied volatility is a crucial element of any financial toolbox, since it is used for quoting and hedging of options as well as for model calibration. In contrast to the Black-Scholes formula its inverse, the implied volatility, is not explicitly available and numerical approximation is required. We propose a bivariate interpolation of the implied volatility surface based on Chebyshev polynomials. This yields a closed-form approximation of the implied volatility, which is easy to implement and to maintain.

    We prove a subexponential error decay. This allows us to obtain an accuracy close to machine precision with polynomials of a low degree. We compare the performance of the method in terms of runtime and accuracy to the most common reference methods. In contrast to the existing interpolation methods, the proposed method is able to compute the implied volatility for all relevant option data. In this context, numerical experiments confirm a considerable gain in efficiency, especially for large data sets.

    Glau K., Herold P., Madan D: B., Pötz C.: The Chebyshev method for the implied volatility, 2017, preprint available on arXiv:1710.01797

    • About Kathrin Glau

    Is currently a Lecturer in Financial Mathematics at Queen Mary University of London. Between 2011 and 2017 she was Junior Professor at the Technical University of Munich. Prior to this she worked as a postdoctoral university assistant at the chair of Prof. Walter Schachermayer at the University of Vienna. In September 2010 she completed her Ph.D. on the topic of Feynman-Kac representations for option pricing in Lévy models at the chair of Ernst Eberlein.

    Her research is driven by the interdisciplinary nature of computational finance and reaches across the borders of finance, stochastic analysis and numerical analysis. At the core of her current research is the design and implementation of complexity reduction techniques for finance. Key to her approach is the decomposition of algorithms in an offline phase, which is a learning step, and a fast and accurate online phase. The methods range from model order reduction of parametric partial differential equations to learning algorithms and are designed to facilitate such diverse tasks as uncertainty quantification and calibration, real-time pricing, real-time risk monitoring, and intra-day stress testing.

    • This seminar is kindly hosted by Thomson Reuters.
      The London Quant Group is very grateful to Thomson Reuters for hosting this event
    • Thomson Reuters
      30 South Colonnade,
      Canary Wharf
      E14 5EP
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