In today's equity derivatives market the trend is clearly leading towards long dated multi-asset products with strong path dependency. The purpose of this article is to present a Monte Carlo framework allowing to value and risk manage these products.
The framework accurately reproduces a given Vanilla options market while being as computationally efficient as a standard Monte Carlo routine sampling log-normally distributed assets. Sensitivities to a changing market are readily available since no calibration of model parameters is required.
The framework can be extended to capture additional market information such as basket and forward starting Vanilla option prices. This is achieved by modeling spatial and temporal correlation skew using copulas.