Rates

The Swap-curve framework is based on OIS, FRA, SWAP basis spread, and SWAP market prices. It uses a combination of synthetic deposits, OTC FRA, and SWAP rates to build curves that implement basis spread correctly from beginning to end.

To illustrate this, let's consider the example of building a 6-month Euribor Swap curve. The first instrument we can use is the 6-month Euribor fixing or FRA0x6. Using deposit or shorter Euribor rates would not implement the basis spread correctly.

Synthetic deposits are calculated from OIS forward rates and known OTC FRA rates to create a smooth short-term curve. Backward extrapolation from the first known rate is used to calculate synthetic deposits.

To solve for short-term interest rates, the following equation is used:

(1 + rt) = (1 + OISt) * (1 + ON*t * x)

To calculate synthetic deposits for unknown terms, the ON-x basis is approximated using a polynomial function of degree x, typically 3:

ON-x = α + β * x + γ * x^2

By solving for coefficients α, β, and γ, synthetic deposits can be obtained using the following formula:

Synthetic Deposit = (1 - β * t - γ * t^2) / (1 + r * t)

Finally, the SWAP curve is created by applying synthetic deposits and OTC FRA rates using a discount calculation method.

Overall, this Swap-curve framework allows for accurate valuation and risk assessment of financial instruments, particularly those with basis spread components, by using a combination of synthetic deposits, OTC FRA, and SWAP rates to build curves that reflect market conditions accurately.

The Ready-to-use yield curves for cross-currency swaps offered by our solution provide a straightforward and working solution for Treasury Management Systems that do not natively support curve building. The discount curves are available for several currencies, including CAD, DKK, EUR, GBP, NOK, SEK, and USD.

Each discount curve is based on several rate sets, making curve building a complex process that is rarely supported by any Treasury System. For example, to create a 3-month swap curve from home and foreign currencies, an OIS curve from the home currency, foreign exchange spread information, and the spread curve for long-term tenors are required. In addition, spread information must be extracted from foreign exchange forwards for short-term tenors.

To create floating-leg future cash flows, our solution provides Raw Data and Advanced Rate portfolios, which can be used to build future cash flows accurately.

Overall, ours olution provides a comprehensive and reliable solution for building yield curves for cross-currency swaps, which can be integrated with existing Treasury Management Systems to support accurate financial analysis and risk management.

OIS-adjusted zero coupon curves are necessary for the valuation process because they provide a more accurate reflection of market conditions and the underlying risks of financial instruments.

The Overnight Indexed Swap (OIS) rate is the rate at which banks lend and borrow funds overnight, collateralized against central bank reserves. OIS rates are considered risk-free because they eliminate counterparty credit risk, an important consideration in valuing financial instruments.

In contrast, traditional zero coupon curves are constructed using swap rates that incorporate a credit risk premium, which can make them less accurate for valuing instruments that are collateralized against risk-free assets, such as government bonds.

Using OIS-adjusted zero coupon curves, the valuation model can better reflect the actual risk-free rate and eliminate any distortion caused by credit risk premiums. This can lead to more accurate pricing and risk management decisions and reduce potential losses caused by incorrect valuations.

In summary, OIS-adjusted zero coupon curves are important in the valuation process because they provide a more accurate reflection of market conditions and the underlying risks of financial instruments, particularly those that are collateralized against risk-free assets.

The Calculation Engine offers a range of generic, financial, and helper functions that can be used in corporate ERP- and Treasury Management- Systems. These functions include date functions, interpolation methods, financial functions like interest days and year fraction, currency spread extraction, foreign exchange cross rates, and helper functions like median, matrix covariance, and standard deviation.

The engine also includes a simple formula that allows us to define functions for adding, subtracting, multiplying, and dividing rates. This helps us customize the engine to their specific needs and requirements.

The Advanced Curve Builder feature offers additional functionality for creating more complex curves, such as basis swap curves, cross-currency swap curves, bootstrapped zero coupon curves (with and without OIS discounting), and forward curves (with and without OIS discounting). These curves can be used to value financial instruments accurately and assess their associated risks.

Overall, the Calculation Engine offers a comprehensive set of tools and functions for financial calculations and curve building, which can be integrated with existing corporate ERP- and Treasury Management- Systems to support accurate financial analysis and risk management.