Yield Curven Construction

Interest rate curves have many different types. Sometimes they are quite confusing. There are two main categories in the market: market observed interest rate curves and derived interest rate curves.

The term structure of interest rates, also known as yield curve, is defined as the relationship between the yield-to-maturity on a zero coupon bond and the bond’s maturity. Zero yield curves play an essential role in the valuation of all financial products.

Zero rate curves, also called spot rate curves, are special and dominant type of yield curves. By definition, a zero rate curve is the term structure of the yields-to-maturity of zero coupon bonds. Given a zero rate, we can derive discount factor easily as:
D(t,T) = exp (-rT)
where D(t,T) is the discount factor at time t for maturity T and r is the continuously compounded zero rate or spot rate between time t and T.

Due to the simple relationship between zero rates and discount factors, zero rate curves become dominant valuation vehicle in the market. If people in financial market talk about interest rate curves, yield curves, zero rate curves, or spot rate curves, they actually mean the same thing. Without loss of generality, we will use zero rate curves representing all yield curves. Zero rate curves also have several different types. A zero curve derived from a base swap rate curve is used for discounting, so it is equivalent to discount curve. Similarly, a zero rate curve bootstrapped from a basis swap curve is used to compute forecasting rates. Understanding interest rate curves is essential in financial markets.

Prior to the 2007 financial crisis, financial institutions performed valuation and risk management of any interest rate derivative on a given currency using a single-curve approach. This approach consisted of building a unique curve and using it for both discounting and forecasting cashflows.

However, after the financial crisis, basis swap spreads were no longer negligible and the market was characterized by a sort of segmentation. Consequently, market practitioners started to use a new valuation approach referred to as multicurve approach, which is characterized by a unique discounting curve and multiple forecasting curves

The current methodology in capital markets for marking to market securities and derivatives is to estimate and discount future cash flows using rates derived from the appropriate term structure. The zero term structure is increasingly used as the foundation for deriving relative term structures and as a benchmark for pricing and hedging.

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