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Imposing no‐arbitrage conditions in implied volatilities using constrained smoothing splines
Author(s) -
Laurini Márcio Poletti
Publication year - 2011
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.877
Subject(s) - smoothing , arbitrage , monotonic function , convexity , econometrics , economics , mathematical economics , mathematical optimization , smoothing spline , mathematics , financial economics , statistics , spline interpolation , mathematical analysis , bilinear interpolation
We apply constrained smoothing B‐splines to the construction of arbitrage‐free implied volatilities and derived measures. The constrained smoothing B‐splines allows the imposition of the constraints of monotonicity and convexity given by the no‐arbitrage conditions in the pricing function. We illustrate the methodology in the construction of implied volatilities and also in the construction of derived measures such as risk‐neutral densities, showing that it can be used as an effective tool for general treatment of option prices. Copyright © 2011 John Wiley & Sons, Ltd.