Zero coupon curve

A zero-coupon curve is used to construct interest rates for different maturities that meet equation F C t = ( 1 + i ) t {\displaystyle FC_{t}=(1+i)^{t}} which corresponds to the amount to be paid (FC) for a monetary unit borrowed today and returned at time t. Both the interest rate i and t are expressed in years. The inverse of FC is:

1 F C t = F D t = ( 1 + i ) & # x2212; t {\displaystyle {1 \over FC_{t}}=FD_{t}=(1+i)^{-t}}

The values F D t {\displaystyle FD_{t}} are called discount factors.

Unlike other types of interest rate curves, for example Euribor at 1 month, 3 months, etc. or the swap curve or the government bond yield curve, is not a curve that is directly observable in financial markets, especially for terms longer than one year.

But this curve is very important because it greatly simplifies the development and mathematical formulation and calculation of valuation of all types of financial instruments.

From the different observable curves in the market (money market, interest rate swaps, etc.), the zero coupon curve is constructed. Different methodologies are used for its calculation and, in particular, estimation for unobservable points of the type curve, such as bootstrapping.

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