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A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps

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Listed:
  • Liyuan Jiang
  • Shuang Zhou
  • Keren Li
  • Fangfang Wang
  • Jie Yang

Abstract

We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S\&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approach outperforms the existing nonparametric quartic B-spline and cubic spline methods, as well as the parametric method based on the Normal Inverse Gaussian distribution. As an application, we use the proposed density estimator to price long-term variance swaps, and the model-implied prices match reasonably well with those of the variance future downloaded from the CBOE website.

Suggested Citation

  • Liyuan Jiang & Shuang Zhou & Keren Li & Fangfang Wang & Jie Yang, 2018. "A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps," Papers 1808.05289, arXiv.org, revised Feb 2019.
    • Handle: RePEc:arx:papers:1808.05289
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    References listed on IDEAS

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