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Estimation of Risk-Neutral Density Surfaces

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  • A. M. Monteiro

    ()
    (GEMF/Faculdade de Economia, Universidade de Coimbra, Portugal)

  • R. H. Tütüncü

    (Goldman Sachs Asset Management)

  • L. N. Vicente

    (CMUC, Department of Mathematics, University of Coimbra, Portugal)

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    Abstract

    Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating risk-neutral densities associated with several maturities. Our method uses bicubic splines in order to achieve the desired smoothness for the estimation and an optimization model to choose the spline functions that best fit the price data. Semidefinite programming is employed to guarantee the nonnegativity of the densities. We illustrate the process using synthetic option price data generated using log-normal and absolute diffusion processes as well as actual price data for options on the S&P500 index. We also used the risk-neutral densities that we computed to price exotic options and observed that this approach generates prices that closely approximate the market prices of these options.

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    File URL: http://gemf.fe.uc.pt/workingpapers/pdf/2010/gemf_2010-06.pdf
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    Bibliographic Info

    Paper provided by GEMF - Faculdade de Economia, Universidade de Coimbra in its series GEMF Working Papers with number 2010-06.

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    Length: 35 pages
    Date of creation: Apr 2010
    Date of revision:
    Publication status: Published in Computational Management Science 8(4): 387-414, 2011.
    Handle: RePEc:gmf:wpaper:2010-06

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