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.
Co-Author: Abhimanyu Kumar
Journal: Computational and Applied Mathematics
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