CRM risk: recentering and artefacts

Table of Contents

Summary

The CRM's graph topology has subtle consequences for risk. Because paths couple rates, you cannot bump one pair in isolation — bumping one implies bumps to others reachable through it. To get per-pair risk you recenter the CRM into a star-shaped matrix with the aggregation currency (P&L / accounting / reporting / functional currency) at the centre, every other currency linked directly to it, so a single rate can move without disturbing the rest. Spot-day mismatches along multi-hop paths produce spurious sensitivities (e.g. a NOK Rho on a SEK deal), and aggregation-currency conversion also surfaces theta on the spot roll.

Detail

Bumping a single rate is not local

  • Graph paths mean bumping one rate ripples to others; running risk "by crosses" moves many pairs at once, hiding each cross's individual contribution to, say, an overall USD delta.
  • For the fine-grained per-pair view, switch off the spot-rates graph so one cross moves alone. Running both modes yields cross-effects at the risk level.

Star-shaping around the aggregation currency

  • Recenter so every currency connects directly to the aggregation currency; bumping one rate then doesn't disturb others — the form required for risk.
  • The market movement for a Greek is the percentage move of (Greek currency)/(reporting currency) between two dates, \(\frac{D_1 - D_0}{D_0}\).
  • Can look odd: for a EUR/USD deal with GBP aggregation, movement comes from EUR/GBP and USD/GBP, not EUR/USD.
  • Deltas sum to zero across currencies: bumping all crosses also bumps the aggregation currency, so e.g. USD delta = GBP delta + EUR delta for a EUR/USD deal.
  • A cyclic graph cannot be auto-reduced to a spanning tree (no general prune rule) — ensure the tree by construction.

Multi-hop spot-date mismatch (spurious sensitivities)

  • A derived rate may route through more than two drivers with different spot dates; reconciling needs interest rates + interpolation (see spot date and derivation mechanics).
  • A spot-day mismatch on a path can surface P&L/IR (Rho) sensitivity on a far, unrelated currency — e.g. a NOK Rho on a SEK deal — purely from CRM wiring. It is an artefact (for Bump & Run / Reset there is no real spot sensitivity) and must be understood and, where appropriate, suppressed in attribution.

Theta on the spot roll

  • Aggregation-currency conversion produces theta on settled cash: as spot rolls forward, interest accrues and spot differs, so converting settled cash back to the aggregation currency yields a P&L difference. True for a Forward Spot Roll; a Fixed Roll does not exhibit it.

Risk routing

  • Crosses are split against the more liquid currency (which can differ for spot vs forward), mirroring the CRM's triangulation paths — e.g. SEK/NOK split by the Forward Desk into EUR legs, by the Spot Desk into USD legs. Routing rules decide how trades are split/aggregated to send risk to the right desk (G11 vs EM desks; see currency conventions).

See also

Emacs 29.3 (Org mode 9.6.15)