Pricing Models - How are Cross Spreads Triangulated?

Crosses can be priced as direct crosses or triangulated, see Pricing Models - Pricing Crosses to understand the difference and how to configure each.

For triangulated crosses, only the quantities available are configurable. Unlike direct crosses, the spread can not be manually entered and instead are calculated from the associated drivers bids/offers.

Cross spread Calculation

Spread quantities for both drivers and crosses are quoted in LHS therefore when triangulating between instruments, the quantities will differ and so often a portion of the next tier will be included in the calculation.

Example (simplified):

GBPUSD and USDJPY are both priced at 500k, however 500k GBP = ~636k USD (at GBPUSD 1.27160 spot rate)

Therefore to triangulate a price for GBPJPY in 500k, we need 500k GBPUSD and 636k USDJPY.

Because the TOB quantity for USDJPY is 500k, spread for the extra 136k (or ~27.2%) of the triangulation has to be taken from the second tier.

Given that the TOB spread for USDJPY is configured to be 0.4pips and the second tier 0.5 pips. Whilst GBPUSD TOB is 0.4 pips:

GBPJPY spread at 500k
= GBPUSD spread at 500k x ((USDJPY spread at 500k x (1 - 0.272)) + (USDJPY spread at tier 2 x 0.272))
= 0.4 x (0.4 x 0.7 + 24.12 x 0.239)
= 0.4 x 0.427

= 0.17 pips / 0.017
(actual calculations are done based on the bids/offers themselves, and not based on spread, so figures are only illustrative)

NB: If the TOB output spread for USDJPY is wider than the configured base spread, then the second tier is scaled by that same factor and included in the triangulation.