Pricing Bermudan Callable Derivatives with Default, Collateral Margining, Funding and Investment Costs

In this research note, we price Bermudan structured derivatives including the consequences of default, collateral margining, funding and investment costs. We use LSA Monte Carlo method for finding MTM for collateral margining along all simulation points. We also find 'default MTM' using LSA which helps us calculate cash flows in case of default. Finally we do a third sweep of LS Monte Carlo to calculate 'final MTM' in which we find the price of the derivative while simultaneously calculating funding/investment costs as they themselves depend upon future value of 'final MTM'. All three sets of LSA Monte carlo take just 5-10 seconds for 50K-100K paths and most of the cost associated with computations is in simulation of OIS rates, and Stochastic basis and calculation of basis functions used later for regressions. We also model correlations between default intensities and between default intensities and OIS/Basis rates with an intention to model wrong/Right way risk to some degree. We also give formulas for calculation of survival probabilities/Default Discount Rates in our setting. We also model credit migrations by mapping default probability bands from rating agencies on default intensities