Abstract:
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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.
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