It is standard practice today to adjust the price of a traded financial instrument for the risk of the counterparty’s or one’s own default, by means of Credit Valuation Adjustments (CVA) and Debit Valuation Adjustments (DVA). Further adjustments are becoming increasingly popular, for instance for the cost of funding (FVA), for the lifetime cost of capital (KVA), or for the cost of initial margin (MVA). A common term covering all these valuation adjustments is XVA.

Calculating these XVAs is of paramount importance to financial institutions – for trade pricing, risk management, accounting, and regulatory capital. At the same time, it is a compute intensive calculation and quantitative analysts are striving to put efficient implementations in place. The first and obvious step is to carefully think about possible mathematical optimisations, before starting to implement the software framework.

This white paper describes major algorithmic optimisations for XVA and illustrates the possible computational savings.

  • XVA calculations: CVA, DVA, FVA, MVA, KVA
  • Contexts: trading, risk management, accounting, capital
  • Smart American Monte-Carlo (Longstaff-Schwartz) techniques
  • Simplifying complex trades and exotics
  • Incremental XVA for what-if analysis
  • Reducing the number of simulation dates
  • Efficient sensitivities calculation