This paper studies impacts of imperfect collateralization on derivatives values.
Firstly, we present a general framework for the analysis in a multi-dimensional diffusion
setting, and then calclate pre-default values of forwards and options for the
numerical experiments. In particular, we investigate no collateral posting and timelagged
collateral posting cases under a stochastic volatility model for the underlying
asset prices and stochastic interest and hazard rate models for the risk-free rate and
default intensities. We also derive an approximation for the density function of the
CVA (Credit Value Adjustment) in the valuation of forward contract with bilateral
counter party risk. Moreover, we allow a stochastic collateral asset value to depend
not only on the underlying contract values, but also on other asset prices such as a
currency different from the payment currency of the underlying contract. Finally,
we also examine the effect of correlations on basket option values with stochastic
volatility and stochastic hazard rate models.