Introduction — A Monte Carlo Framework

Abstract

The semi-analytical single-trade CVA calculations of the previous chapters are computationally very efficient, especially when closed-form option pricing formulas are available. However, when we need to compute CVA for a netting set of derivatives — which is the more common case — this option pricing approach quickly reaches its limits:

• We would need to come up with an option pricing formula for varying underlying derivative portfolios. While this may still be possible for sufficiently simple portolios, each portfolio/trade combination represents a new problem which requires customization, mapping or development efforts.

• When the portfolio is complex and contains structured products, closed-form option pricers are not available anymore, and we would have to resort to numerical techniques for the option price in each case.

• When the portfolio is collateralized, and CSA details have to be taken into account, semi-analytical approaches are not feasible anymore.