The payoff of reverse convertible product involves returns on multiple assets and is conditional on hitting of continuous barriers. The Monte Carlo methodology is an efficient conditioning technique. As this payoff involves continuous barriers, the expectation of this payoff can be calculated using a version of conditional Monte Carlo method. Biased upper and lower estimator bounds plus a biased price placed between these bounds.

The article discusses credit delta (PV01) and credit VaR measurements. Credit value at risk (VaR) is used for measuring and analyzing credit risk of a portfolio. The basic methodology of the Credit VaR employs the credit migration approach spearheaded by RiskMetrics. It assumes that obligor’s credit quality is determined by the obligor’s asset value, which in turn is approximated by its standardized equity return.

For a European compound call option, the payoff at maturity is given by the maximum of the basket level less the strike, and zero. The option price, given by the discounted expected value of the payoff above, is calculated from a Gauss-Hermite quadrature. The model also provides various hedge ratios, which are approximated using finite differencing but based on parallel shifts to the respective independent variables.

This paper presents a model for compute average volatility and correlation. Since an arithmetic average of log-normally distributed variables is not log-normal, We approximate the arithmetic average by matching its first and second moments with those of a log-normal variable. We generate the volatility of a log-normal variable that approximates an arithmetic average of asset prices. We also calculate the correlation between two log-normal variables chosen to match that between two arithmetic averages of asset prices.