PelatihA local correlation model gives each asset its own local volatility, fitted to its own options, and makes the correlation between them a function of time and of the market state, typically the index level: . The function is chosen so that the model’s index options reprice the index smile, which it does by construction in the same way that local volatility fits one asset’s smile.
Contoh
Example 17.12 (Fitting the index skew)
For the synthetic index the fit gives , which reprices the index at 21.93%, 19.19% and 16.99% against 21.93%, 19.19% and 16.98% (Figure 17.2, right). Correlation is 0.91 when the index is 10% down in log terms, capped at one below that, and 0.19 when it is 10% up. The members’ marginal laws are unchanged, lognormal at their own volatilities. Only their dependence moves with the market.