Hi all,I am trying to implement a zero-coupon using the usual practice (based on this document (in french)) and I would like to know which one of the below method do you usually use.Zero coupon yield curve can be classified in three categories [according to counterparties risk (with correct names)] :- The treasury strip (built based of G7 government bonds (with AAA as rating))- The interbank zero-coupon curve (built based on spot rates, futures rates and swaps rates (banks rating between A and AA))- The corporate zero-coupon curve (companies with ratings A or B).The are three different methods to evaluate a zero coupon curve ;(1) Method 1 ("Direct method"): Bootstrapping - (robust and arbitrage free (best to be safe)) The zero-coupon rate is defined by : [$]\begin {equation} B(0,t)= \frac{1}{[1+R(0,t)]^t}\end {equation}[$]where B(0,t) is the market price at t=0 of a zero coupon bond paying $1 at maturity. B(0, t) = discount factor in 0 for the maturity t.R(0,t) = the yield to maturity (ytm) at t = 0 or interest rate of the zero-coupon bond paying $1 at t.R(0,t) = the zero-coupon rate at 0 with a maturity t.The bond price V at the date t is :[$]\begin {equation}V=\sum_{i=t+1}^m \frac {F(i)}{[1+R(i,i-t)]^{i-t}} = \sum_{i=t+1}^m F(i) B(t,i)\end {equation}[$]Construction of the Treasury strip (government zero-coupon curve)Chosen government bonds (for the calculation of the zero coupon) must have the same coupon dates, and have their maturities as multiple of the coupons frequencies.However, in practice it is difficult to find bonds that have these features.Notation and resolution[$]P_{t}=(P_{t}^1, P_{t}^2, ..., P_{t}^n)^T[$] = the vector of price at the date t for n (chosen) bonds[$]F=(F_{ti}^{(j)})_{i=1,...,n, j=1,...,n}[$] = an n*n matrix corresponding to the n bonds cash flow.[$]B_{t}=(B(t,t_{1}), B(t,t_{2}),..., B(t,t_{n}))^T[$] = the discount factor vectorThe knowledge of this zero-coupon (built) will allow us to :- evaluate all financial instruments that have deterministic cash flow, - to evaluate the forward rate curve- and the yield to maturity at a par value ("par value", is the amount a bond holder will be paid when it matures. )(2) Method 2.a ("Indirect method") (they are not arbitrage-free)For a chosen number of n bonds as a calibrating instruments, as described in Options, Futures and Other Derivatives (Fifth edition page 564, part 23.14). We have to minimize : [$]\sum_{i=1}^n (U_{i}-V_{i})^{2}[$] (*)Where [$]U_{i}[$] is the market price of the ith calibrating instrument and V_{i} is the price given by the chosen model .(*) is then resolved using the The Levenberg Marquart algorithm (or in practice excel solver).The most common model used for for this method is the Nelson Siegel model, Vasicek model and Cox Ingersoll Ross model.(2) Method 2.b ("Indirect method") Use of splines model and as in method 2.a, we have to minimize a similar equation.

Normally I use method 1 with a large amount of expert judgement regarding the subset of the universe of bonds used to do the fitting, and the Smith-Wilson algorithm to fit a continuous curve.But it depends on your aim - approach 2 is good if it is advantageous to you to represent the yield curve using some simple functional form (with few parameters)

I would echo chewwy's response... Dunno about the second method, though.

Definitively, method 1 remains the safer method.