Building OIS Curves and Discounting OIS Swap Cash Flows
Summary
The document explains how an OIS fixed rate is determined by constructing curves that value the compounded overnight floating leg. Depending on currency and tenor, market inputs may combine outright OIS swaps at shorter maturities with IBOR swaps and IBOR–OIS basis swaps farther out, or may use outright OIS swaps throughout. Curve stripping follows standard bootstrapping logic, with added care needed because the floating coupon compounds daily fixings.
For a swap collateralized in its own currency, the example uses the same OIS curve to project overnight coupons and discount cash flows. If collateral is in another currency, the appropriate collateral-adjusted curve must account for the relevant overnight rates and cross-currency basis; a choice among collateral currencies adds complexity. The response gives a conceptual framework rather than a full numerical bootstrapping recipe, and its descriptions of market conventions are currency-dependent rather than universal.
Key ideas
- OIS floating coupons depend on daily compounded overnight fixings, so their value requires an overnight curve.
- Curve inputs vary by currency and maturity and can include outright OIS swaps and basis instruments.
- Curve stripping resembles standard curve construction but must price the compounded floating leg correctly.
- For same-currency collateral, the example uses the OIS curve for both projection and discounting.
- Cross-currency collateral requires collateral-adjusted discounting that reflects overnight rates and basis.
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# OIS Fixed Rate - how to calculate on trade booking? # OIS Fixed Rate - how to calculate on trade booking? I am trying to understand how the Fix rate on a OIS trade is calculated at trade initiation. I understand this process for a Fixed V LIBOR trade non collateralized ( discount and projection curve are the same ) but get somewhat confused here Particularly in reference to the curve that is used, what are the instruments used to build from, how is it built, is the same curve then used for discounting the cashflows as projection. Thanks ## Answer by oronimbus (score 1) https://quant.stackexchange.com/a/51606 The idea of pricing a Fixed-to-Float IBOR swap is very similar to that of an OIS swap. The only difficulty is determining the present value of the OIS leg since now each payment depends not just on one (in-advance) IBOR fixing but a (daily) compounded OIS rate. That means the final value of an OIS payment is not known until all fixings have occurred. That's where the curve comes in: Depending on the currency, the OIS curve either consists of a mix of outright OIS swaps on the front end (~6 years) and IBORvOIS basis swaps for the long end (combined with IBOR swaps to get a 'fixed' equivalent) or purely outright OIS swaps. An example for the former is USD and for the latter EUR. I haven't seen an OIS curve that uses OIS futures, although they do trade. The method of stripping the curve is similar to any other curve with the additional difficulty of correctly pricing the floating OIS leg. Example: Say you have a 1y EUR OIS swap with EUR collateral. You project cashflows using the EONIA curve and since you're using EUR collateral you will discount cashflows with the same curve. Now if your collateral were GBP things get more complicated. Because now you not only need to consider EONIA but also SONIA, as well as the basis between EUR and USD, i.e. you'd need a CSA adjusted collateral curve (refer to here for more details). It gets even more tricky if you can choose between a basket of collateral currencies (say USD, GBP and EUR), for an overview refer to here.
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