When to use Local Volatility Models? When to use Stochastic Volatility Models?

[chengcj]

I understand that Stochastic Vol Models should be used when Exotic Option payoff is Volatility dependent (such as Variance Swaps and Volatility Swaps).

Stochastic Vol Models should also be used when Exotic Option has forward starting features (such as Cliquet Options). Can someone explain why should we use Stochastic Vol Models for forward starting options?

Also, given an Exotic Option, how would you decide whether to use Local Vol or Stochastic Vol models for pricing?

 

[financeguy]

I understand that Stochastic Vol Models should be used when Exotic Option payoff is Volatility dependent (such as Variance Swaps and Volatility Swaps).

Stochastic Vol Models should also be used when Exotic Option has forward starting features (such as Cliquet Options). Can someone explain why should we use Stochastic Vol Models for forward starting options?

Also, given an Exotic Option, how would you decide whether to use Local Vol or Stochastic Vol models for pricing?

You have to use a stochastic vol model (well, really a blended stochastic/local vol model) if the option is path dependent. If the option is not path dependent, purely European style, then you can use a local vol model. I should point out though that above you stated you needed a stochastic vol model to price a variance swap - this is not the case as you should be able to use the vanilla replication along with the smile on the expiration date to price it. This means a variance swap has no model dependence, but does rely on the way you construct your smile (the interpolation and extrapolation of points on the smile).