Definition of 'Local Volatility'
A model used in quantitative finance to calculate the unpredictability of the underlying current asset of a financial derivative. Because of the treatment of the underlying asset price as the sole random variable, local volatility models are not suitable for the pricing of all options, such as cliquet options.
Local variance, another calculation used in quantitative finance, is the square of local volatility.
Investopedia explains 'Local Volatility'
Local volatility models are often used alongside stochastic volatility models in order to compare assumptions on different derivative valuations. The local volatility model "knows" volatilities in advance, while in stochastic volatility models volatility is treated as an uncertainty. The concept of local volatility was put forth by Emanuel Derman and Iraj Kani.