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Scaling providesdensities at other maturities. Stochastic processes with these marginalsare identified. In addition to a specific local volatility modelthe densities are consistent with the difference of compoundexponential processes taken at log time and scaled by the square root oftime. The underlying process has a single parameter, the davanced rate of the process. Delta hedging using Laplacian andAsymmetric Laplacian implied volatilities are developed and comparedwith Black Merton Scholes implied volatility hedging.The hedgingstrategies are implemented for stylized businesses represented bydynamic volatility indexes.
The Laplacian hedge is seen to be smootherfor the skew trade.
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