Stochastic collocation reveals flaws in local volatility model for asset pricing.
The article explores using a method called stochastic collocation for assets that have a lower boundary. It finds that using polynomial collocation for a lognormal distribution doesn't work well. The study also looks at issues with the collocated local volatility model. Finally, it presents a simple formula for the Dupire local volatility derived from option prices using stochastic collocation.