Why OIS-Based Discounting Serves as a Reference for Derivative Valuation
Summary
The answer explains why a discount curve described as risk-free is used in derivative valuation even though the valued instrument can carry market and liquidity risk. It frames the curve as a reference rate for replication and comparison: in a replication argument, funds associated with an option or security are assumed to earn the chosen benchmark. Changes in other rates relative to that reference can then be interpreted as repricing of the assets being compared. This helps explain the use of OIS discounting after LIBOR ceased to be treated as a suitable risk-free proxy.
The answer stresses that the benchmark is not literally free of risk. It cites residual collateral transaction risk and argues that government bond yields can also be distorted by default concerns and liquidity effects, including unusually strong demand for on-the-run Treasuries. These are conceptual explanations, not a complete derivation of multi-curve valuation or a claim that one curve suits every collateral arrangement. The appropriate benchmark depends on the replication and market conventions being modeled.
Key ideas
- A discount curve provides a benchmark rate for replication and valuation comparisons.
- Rates moving relative to the benchmark can reflect repricing specific to other assets.
- OIS became a common reference after LIBOR was no longer treated as a risk-free proxy.
- The chosen curve still has risks and depends on market and collateral conventions.
- Government yields can be affected by default and liquidity effects, which may distort valuations.
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Full text
# Why should the Discount Curve be risk-free? # Why should the Discount Curve be risk-free? I have read up about the discount curve that is being used to value securities. The multi-curve methodology for valuing derivatives was mainly adopted because LIBOR was no longer seen as a proxy for risk-free yield (and hence the OIS curve is now used). What I am trying to understand is why should the discount curve that is being used to value a security/ derivative ( such as an Interest rate swap) be risk-free/ proxy for risk-free, since the security is not risk-free, regardless of whether there is collateral or not (e.g. market risk, liquidity risk etc. will still be present)? ## Answer by Si Chen (score 1) https://quant.stackexchange.com/a/68333 The discount curve is not truly risk free, but it's called "riskfree" because it's A) where you would invest your funds while replicating an option or security and B) it serves as a reference point for valuing other assets. So for example if you're replicating a swaption, then the assumption is that you're holding the premium and earning LIBOR or its replacement, which over the term of the option is the swap rate. Also it's considered "riskfree" so that any rate that changes relative to it could be considered a repricing of a specific asset, rather than a repricing of your reference rate. This is helpful to look at the comparative repricings of assets over time, for example swap spreads on different types of bonds. It's not truly "riskfree" because a swap is a transaction between 2 commercial banks, so there is some collateral transaction risk. However, it is a pretty good option. For example it is more objective than government bonds, which have default risks but also liquidity risks, so a discount curve constructed from government bond yields could cause more biases. In particular "on the run" treasuries could have artificially low yields because of their demand as hedging instruments, and using them could distort your values for long-term options and bonds with embedded options.
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