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Activity Number: 492 - Application of Nonparametric Methods
Type: Contributed
Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Nonparametric Statistics
Abstract #310925
Title: A New Nonparametric Estimator for the State Price Density
Author(s): Yating Wan* and Chenxu Li and Xiaojun Song
Companies: Peking University Guanghua School of Management, Business Statistics and Peking University Guanghua School of Management, Business Statistics and Peking University Guanghua School of Management, Business Statistics
Keywords: state price density; nonparametric estimation; moment conditions; leverage effect; tail estimates; risk management
Abstract:

We propose a new nonparametric estimator for the state price density, which is an important financial quantity for derivatives pricing and risk management. Our method does not require to impose any parametric assumptions and thus is fully model-free. More importantly, our estimator is the first attempt to incorporate Lee (2004)'s moment conditions for the tail regions, which guarantee to deliver more accurate tail estimates. Indeed, our estimation results display more accurate interpolation and in particular extrapolation at tails beyond the available data range. In addition, our results provide parameter estimates that support the leverage effect on volatility, and verify a well-established property of the state price density. Lastly, the stylized facts of negative skewness and fat tails, which are adequately captured by our proposed estimator of the state price density, also highlights the applicability of our estimator to the tail risk management. In particular, while alternative purely nonparametric methods lead to an underestimation of tail risks, our proposed estimator is able to uncover such underestimation and thus crucial to ensuring minimum capital requirements.


Authors who are presenting talks have a * after their name.

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