Sieve estimation of option implied state price density
Files
First author draft
Date
2018-11-14
DOI
Authors
Qu, Zhongjun
Lu, Junwen
Version
First author draft
OA Version
Citation
Zhongjun Qu, Junwen Lu. "Sieve Estimation of Option Implied State Price Density."
Abstract
The state price density, as a central concept in asset pricing, embodies rich information about
market expectations and risk attitudes. The paper develops a nonparametric estimator for this
density using a single cross section of European option prices. The estimator has two features
that di erentiate it from other methods in the literature. First, it uses information from both call
and put option prices. Second, it does not require estimating any second order derivative. The
estimator is characterized by the solution to a constrained and penalized linear regression. The
technical analysis faces two challenges because the density is de ned by the Fredholm integral
equation of the rst kind with an unbounded support, and the kernel functions are unbounded
and non-di erentiable. We address these challenges by exploiting the structure of the option
pricing problem. After establishing the consistency and the convergence rate of the estimator,
we apply it to estimate the state price densities implied by S&P500 index options and by the
VIX options. The sample periods include the recent nancial crisis and the Great Recession,
during which the market turbulence imposes substantial challenges for adaptive estimation. We
show that the procedure can work with both daily and high frequency observations. We also
study whether quantiles of this density have predictive power for future return distributions.