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Imposing No-Arbitrage Conditions In Implied Volatility Surfaces Using Constrained Smoothing Splines
Código: WPE – 096
Márcio Poletti Laurini
We apply the constrained smoothing b-splines introduced by [He & Ng, 1999] to the construction of arbitrage-free implied volatility surfaces extracted from option price data. The constrained smoothing bsplines permits to impose the constraints of monotonicity and convexity given by the option pricing equation and are related to no-arbitrage conditions in the construction of smoothed implied volatility surfaces. The methodology share the robustness properties of quantile regression methods, as the method formulates the b-spline using LP projections. We illustrate the methodology through the calculation of implied volatility surfaces free of arbitrage, and also for the calculation of local volatilities and risk neutral densities, showing that the methodology also can be used as a pre-processing tool for general treatment of option data.