The 2007 financial crisis, market practitioners assumed that interbank lending rates like LIBOR were effectively risk-free. The "risk-free" LIBOR curves were used as discount curves for the valuation of derivatives whose cash flows were believed to be risk-free, following the well-known finance principal of matching the discount rate to the cash flow. (For more, see: Discounted Cash Flow - DCF).

In the wake of the crisis, the market realized that some derivative cash flows and LIBOR discount curves aren't free of risk. Unsecured derivative cash flows are subject to counterparty credit risk; that a counterparty will not make contractual payments. Moreover, LIBOR rates incorporate a counterparty credit risk premium which varies depending on the economic environment. It's particularly important to note that the risk premium increases significantly during a financial crisis and has been found to be non-negligible in normal conditions.

The acknowledgement of counterparty risk means that conventional valuation techniques must be reconsidered and modified to reflect the true risk of a trade. Where a derivative trader's position is fully exposed to counterparty risk, it may be reasonable to discount the cash flows of that instrument using a credit-risky LIBOR discount curve. This approach is sensible if the derivative cash flows are funded at LIBOR and if the credit risk of the counterparty is similar to that of the interbank market. If the funding rate or the credit risk differs, a different approach should be used in order to maintain consistency.

For derivative positions that have limited counterparty risk, like collateralized trades with daily collateral calls, the funding rate is assumed to be the rate earned on the collateral. In most cases, the collateral rate is an overnight rate of return such as the Federal Funds rate. Thus the most appropriate discount curve to use in the case of collateralized derivatives is the overnight curve constructed from overnight indexed swap (OIS) rates.

The use of an overnight discount curve is known as "OIS discounting" and is commonly used for interest rate derivatives like interest rate swaps and cross-currency swaps. Although far less common, some market participants make use of OIS discounting for derivatives of other asset classes. When a trader switches from using a LIBOR discount curve to an OIS curve, the change in derivative valuations will have either a positive or negative profit and loss (P&L). (For more on OIS discounting, see: An Introduction to OIS Discounting).

The overnight curve can be thought of as the LIBOR curve without a counterparty credit risk premium. The result is that the overnight curve characterizes a downward shift of the LIBOR curve. But the downward shift is not parallel in nature - the credit spread typically widens as the maturity increases (as shown in the graph below). This is because the risk of non-payment increases with time.

The downward shift of the discount curve leads to higher discount factors but the valuation impact can be either positive or negative.

In the case of interest rate swaps and cross-currency swaps, the difference in valuation will depend on whether the swap is in- or out-the-money. Under OIS discounting - provided the swap cash flows are determined independently of the overnight curve - a swap that is in-the-money will be deeper in-the-money and a swap that is out-the-money will be deeper out-the-money. It is also possible that swaps may have a non-zero day one P&L if market makers still make use of LIBOR discount curves for pricing purposes (this is the case in some less developed markets). If market makers make use of OIS discounting when pricing, the swap will price to par and there will be no P&L on trade date.

If options are collateralized and the option margin earns an overnight rate, OIS discounting can be applied. Call options (or interest rate caplets) will have lower values and put options (or interest rate floorlets) will have higher values. Again, this relationship is true only if the option cash flows are determined independently of the overnight curve. (To learn more about options, read Options Basics).

In the wake of the crisis, the market realized that some derivative cash flows and LIBOR discount curves aren't free of risk. Unsecured derivative cash flows are subject to counterparty credit risk; that a counterparty will not make contractual payments. Moreover, LIBOR rates incorporate a counterparty credit risk premium which varies depending on the economic environment. It's particularly important to note that the risk premium increases significantly during a financial crisis and has been found to be non-negligible in normal conditions.

The acknowledgement of counterparty risk means that conventional valuation techniques must be reconsidered and modified to reflect the true risk of a trade. Where a derivative trader's position is fully exposed to counterparty risk, it may be reasonable to discount the cash flows of that instrument using a credit-risky LIBOR discount curve. This approach is sensible if the derivative cash flows are funded at LIBOR and if the credit risk of the counterparty is similar to that of the interbank market. If the funding rate or the credit risk differs, a different approach should be used in order to maintain consistency.

For derivative positions that have limited counterparty risk, like collateralized trades with daily collateral calls, the funding rate is assumed to be the rate earned on the collateral. In most cases, the collateral rate is an overnight rate of return such as the Federal Funds rate. Thus the most appropriate discount curve to use in the case of collateralized derivatives is the overnight curve constructed from overnight indexed swap (OIS) rates.

The use of an overnight discount curve is known as "OIS discounting" and is commonly used for interest rate derivatives like interest rate swaps and cross-currency swaps. Although far less common, some market participants make use of OIS discounting for derivatives of other asset classes. When a trader switches from using a LIBOR discount curve to an OIS curve, the change in derivative valuations will have either a positive or negative profit and loss (P&L). (For more on OIS discounting, see: An Introduction to OIS Discounting).

**Implications for Valuations**The overnight curve can be thought of as the LIBOR curve without a counterparty credit risk premium. The result is that the overnight curve characterizes a downward shift of the LIBOR curve. But the downward shift is not parallel in nature - the credit spread typically widens as the maturity increases (as shown in the graph below). This is because the risk of non-payment increases with time.

The downward shift of the discount curve leads to higher discount factors but the valuation impact can be either positive or negative.

**Interest Rate Swaps and Cross-Currency Swaps**In the case of interest rate swaps and cross-currency swaps, the difference in valuation will depend on whether the swap is in- or out-the-money. Under OIS discounting - provided the swap cash flows are determined independently of the overnight curve - a swap that is in-the-money will be deeper in-the-money and a swap that is out-the-money will be deeper out-the-money. It is also possible that swaps may have a non-zero day one P&L if market makers still make use of LIBOR discount curves for pricing purposes (this is the case in some less developed markets). If market makers make use of OIS discounting when pricing, the swap will price to par and there will be no P&L on trade date.

**Options**If options are collateralized and the option margin earns an overnight rate, OIS discounting can be applied. Call options (or interest rate caplets) will have lower values and put options (or interest rate floorlets) will have higher values. Again, this relationship is true only if the option cash flows are determined independently of the overnight curve. (To learn more about options, read Options Basics).

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