Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity |
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| Authors: | Ana Margarida Monteiro Reha H Tütüncü Luís N Vicente |
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| Institution: | 1. Faculdade de Economia, Universidade de Coimbra, Av. Dias da Silva, 165, 3004-512 Coimbra, Portugal;2. Department of Mathematical Sciences, 6113 Wean Hall, Carnegie Mellon University, Pittsburgh, PA 15213, USA;3. Departamento de Matemática, Universidade de Coimbra, 3001-454 Coimbra, Portugal |
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| Abstract: | We present a new approach to estimate the risk-neutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting optimization problem, used to invert the data and determine the corresponding density function, is a convex quadratic or semidefinite programming problem, depending on the formulation. Both of these problems can be efficiently solved by numerical optimization software. |
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| Keywords: | Option pricing Risk-neutral density estimation Cubic splines Quadratic programming Semidefinite programming |
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