6533b833fe1ef96bd129c327
RESEARCH PRODUCT
COMPUTATION OF LOCAL VOLATILITIES FROM REGULARIZED DUPIRE EQUATIONS
Elisabeth RöslerMartin Hankesubject
Mathematical optimizationMathematicsofComputing_NUMERICALANALYSISBlack–Scholes modelFunction (mathematics)Inverse problemBlack–Scholes model Dupire equation local volatility inverse problem regularization numerical differentiationRegularization (mathematics)Tikhonov regularizationLocal volatilityComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONNumerical differentiationApplied mathematicsGeneral Economics Econometrics and FinanceFinanceLinear equationMathematicsdescription
We propose a new method to calibrate the local volatility function of an asset from observed option prices of the underlying. Our method is initialized with a preprocessing step in which the given data are smoothened using cubic splines before they are differentiated numerically. In a second step the Dupire equation is rewritten as a linear equation for a rational expression of the local volatility. This equation is solved with Tikhonov regularization, using some discrete gradient approximation as penalty term. We show that this procedure yields local volatilities which appear to be qualitatively correct.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-03-01 | International Journal of Theoretical and Applied Finance |