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Quantitative Finance · Glossário

O que é Collateral choice option?

Definition 2.10 Rates, Credit, XVA and Risk · Capítulo 2 — Multi-Curve and Collateral Discounting

A collateral choice option is the right of the collateral poster to choose, and later change, which of several eligible collaterals it posts. Expressed in the trade’s currency, the poster chooses the collateral earning the highest rate, so the trade is discounted at max⁡ict(i)\max_i c^{(i)}_t over the eligible collaterals.

Instantaneous forward rates earned by two eligible collaterals, in dollars, and the effective discount rate when the poster may choose. The lines cross at 7.5 years (dashed), where the illustrative basis changes sign. Data: the chapter’s tutorial.
Figure 2.3. Instantaneous forward rates earned by two eligible collaterals, in dollars, and the effective discount rate when the poster may choose. The lines cross at 7.5 years (dashed), where the illustrative basis changes sign. Data: the chapter’s tutorial.

Exemplos

Example 2.11 (A dollar trade with a two-currency CSA)

Take an illustrative basis of −15-15 basis points at the front rising linearly to +5+5 at ten years. Euros are the better collateral until 7.5 years, dollars after. A payment of USD 100 million in ten years is worth USD 68 598 292 under a dollar-only CSA and USD 68 213 510 when the payer may post either currency: the choice, used at every date, raises the effective discount rate by an average of 56.25/10=5.656.25/10 = 5.6 basis points a year and costs the receiver USD 384 782. With volatile rates and basis the option is worth more than this intrinsic value.

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