Local Volatility - Use

Use

Local volatility models are useful in any options market in which the underlying's volatility is predominantly a function of the level of the underlying, interest-rate derivatives for example. Time-invariant local volatilities are supposedly inconsistent with the dynamics of the equity index implied volatility surface, but see Crepey, S (2004). "Delta-hedging Vega Risk". Quantitative Finance 4., who claims that such models provide the best average hedge for equity index options. Local volatility models are nonetheless useful in the formulation of stochastic volatility models.

Local volatility models have a number of attractive features. Because the only source of randomness is the stock price, local volatility models are easy to calibrate. Also, they lead to complete markets where hedging can be based only on the underlying asset. The general non-parametric approach by Dupire is however problematic, as one needs to arbitrarily pre-interpolate the input implied volatility surface before applying the method. Alternative parametric approaches have been proposed, notably the highly tractable mixture dynamical local volatility models by Damiano Brigo and Fabio Mercurio.

Since in local volatility models the volatility is a deterministic function of the random stock price, local volatility models are not very well used to price cliquet options or forward start options, whose values depend specifically on the random nature of volatility itself.