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Local volatility is a model used in derivative pricing to describe how the underlying asset’s volatility varies with both its current price and with time. While it can be fit to a smile at a particular time, the model is static and therefore does not capture volatility dynamics over time. It was introduced in 1994 by Bruno Dupire in his Risk paper ‘Pricing with a smile’. Its purpose was to explain the skew in volatility values with respect to underlying asset price. Typically, the implied volatility increases as the price diverges from the strike leading to a characteristic smile shape – hence its name ‘volatility smile’. This smile is not necessarily symmetrical about the strike but will be more symmetrical for symmetric products like those in foreign exchange.
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