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    Recovery of time-dependent volatility in option pricing model

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    Article (2.409Mb)
    Date
    2016-09-29
    Author
    Deng, Zui-Cha
    Hon, Y. C.
    Isakov, Victor
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    Citation
    Deng, Zui-Cha; Hon, Y. C.; Isakov, Victor, 1947-. 2016. Recovery of time-dependent volatility in option pricing model. Inverse Problems, vol. 32:no. 11
    Abstract
    In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective.
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    URI
    http://dx/doi/org/10.1088/0266-5611/32/11/115010
    http://iopscience.iop.org/article/10.1088/0266-5611/32/11/115010/meta
    http://hdl.handle.net/10057/12682
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