2013/06/05 by Sylvain Corlay, Corlay, Sylvain · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Reservoir Engineering and Simulation Methods #Statistical Methods and Inference #Stochastic processes and financial applications #math.PR #q-fin.CP
paper · pdf · doi:10.48550/arxiv.1306.0995
25 pages
openalex publication_date 2013/06/05 · arxiv created 2015/06/12 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines obtained by including basis functions with infinite support. We first come back to the application of shape-constrained B-splines to the estimation of conditional expectations, not merely from a scatter plot but also from the given marginal distributions. An application is the Monte Carlo calibration of stochastic local volatility models by Markov projection. Then we present a new technique for the calibration of an implied volatility surface to sparse option data. We use a B-spline parameterization of the Radon-Nikodym derivative of the underlying's risk-neutral probability density with respect to a roughly calibrated base model. We show that this method provides smooth arbitrage-free implied volatility surfaces. Finally, we sketch a Galerkin method with B-spline finite elements to the solution of the partial differential equation satisfied by the Radon-Nikodym derivative.