This paper presents a new formulation for conveniently extracting the risk-neutral density (RND) function from the scarce data of the call price quotes, in the absence of any standard functional form. The existing sol...
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This paper presents a new formulation for conveniently extracting the risk-neutral density (RND) function from the scarce data of the call price quotes, in the absence of any standard functional form. The existing solutions require primarily estimating the call price function under no-arbitrage conditions and then estimating the RND function. In this exposition, an independent relation is derived from the definition itself that connects RND to the call price function using tools like Laplace transform and Abel's summation formula. This transforms the situation into a regression problem with simple constraints. The resulting linearly constrained least-square minimization problem gives an exact solution for the decision vector. The efficacy and accuracy of the proposed method are tested and validated on S & P 500 option price data.
We suggest a semi-nonparametric estimator for the call-option price surface. The estimator is a bivariate tensor-product B-spline. To enforce no-arbitrage constraints across strikes and expiry dates, we establish suff...
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We suggest a semi-nonparametric estimator for the call-option price surface. The estimator is a bivariate tensor-product B-spline. To enforce no-arbitrage constraints across strikes and expiry dates, we establish sufficient no-arbitrage conditions on the control net of the B-spline surface. The conditions are linear and therefore allow for an implementation of the estimator by means of standard quadratic programming techniques. The consistency of the estimator is proved. By means of simulations, we explore the statistical efficiency benefits that are associated with estimating option price surfaces and state-price densities under the full set of no-arbitrage constraints. We estimate a call-option price surface, families of first-order strike derivatives, and state-price densities for S&P 500 option data. (C) 2014 Elsevier B.V. All rights reserved.
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