Search results for "Local volatility"

showing 2 items of 2 documents

COMPUTATION OF LOCAL VOLATILITIES FROM REGULARIZED DUPIRE EQUATIONS

2005

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.

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 equationMathematicsInternational Journal of Theoretical and Applied Finance
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Building a Consistent Pricing Model from Observed Option Prices

1999

This paper constructs a model for the evolution of a risky security that is consistent with a set of observed call option prices. It explicitly treats the fact that only a discrete data set can be observed in practice. The framework is general and allows for state dependent volatility and jumps. The theoretical properties are studied. An easy procedure to check for arbitrage opportunities in market data is proved and then used to ensure the feasibility of our approach. The implementation is discussed: testing on market data reveals a U-shaped form for the "local volatility" depending on the state and, surprisingly, a large probability for strong price movements.

MicroeconomicsLocal volatilityEconometricsArbitrage pricing theoryEconomicsCall optionFundamental theorem of asset pricingArbitrageVolatility (finance)Implied volatilityRational pricingSSRN Electronic Journal
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