Warning: spot rates are calculated by employing Central Bank Treasuries only. So therefore, the first spot rate is the Internal Rate Of Return of such a theoretical zero coupon treasury, the following spot rates -on the yield curve- undergo a bootstrapping process. Precaución: las tasas de interés al contado se calculan empleando títulos del Banco Central únicamente. Entonces y por lo tanto, la primera tasa al contado es la Tasa Interna De Retorno de un teórico título sin cupones, las tasas al contado siguiente -sobre la curva de rendimientos- se someten un proceso de iteración/recálculo.
La siguiente es la información después de un día de operaciones en el mercado de renta fija en términos anuales. The following information is given by the fixed rent market after an annualized trading day (Oct. 11, 2012):
Fecha de vencimiento/ Spot Rate/Tasa al contado (annual effective):
Maturity Date:
Feb. 15, 2013 0.1250782%
Aug. 15, 2013 0.3967851%
Feb. 15, 2014 0.4751252%
Aug. 15, 2014 0.5253753%
Feb. 15, 2015 0.5163284%
Aug. 15, 2015 0.4922074%
Feb. 15, 2016 0.3917654%
Aug. 15, 2016 0.537439%
Feb. 15, 2017 0.8889277%
Para títulos emitidos por el BANCO CENTRAL. For "treasuries" issued by the Central Bank.
Cuál es la curva de Tasas Instantáneas? What is the Short Rate curve ?
Time to maturity in years/Plazo al vencimiento en años: 0.3479452, 0.8438356, 1.3479452, 1.8438356, 2.3479452, 2.8438356, 3.3479452, 3.8465753, 4.3506849
Habrá que reescribir las tasas de descuento en semestre efectivo y no año efectivo/ You will have to rewrite the rates in effective semesters and not years
La primera tasa instantánea es igual a la primera tasa al contado/The first short rate is equal to the first spot rate: 0.0625195% per semester or 0.0435026% until maturity. r(0,1)
r(1,2) = (1.001981961^2 / 1.000625195)-1 = 0.334057% per semester or 0.2910886% per time fraction
r(2,3) = 0.305232% per time fraction or 0.315497% per semester
r(3,4) = 0.3277799% per time fraction or 0.337568% per semester
r(4,5) = 0.2433175% per time fraction or 0.239787% per semester
r(5,6) = 0.1873067% per time fraction or 0.185672% per semester
r(6,7) = -0.087239% per time fraction or -0.104445% per semester
r(7,8) = 0.7555578% per time fraction or 0.7785148% per semester
r(8,9) = 1.804683% per time fraction or 1.855504% per semester
The short rate curve tells us the market expectation and the expected value for the 3 month rate in 3, 6, 9, 12 months from now and so on OR the annual effective rate in 1, 2, 3, 4 years and so on...../La curva para tasas instantáneas nos dice la expectativa del mercado de un periodo a otro y el valor de la tasa a 3 meses en 3, 6, 9, 12 meses desde ahora y en adelante O la tasa efectiva anual en 1, 2, 3, 4 años y en adelante ...
Ahora la curva de tasas a futuro. Now the forward rate curve.
f(1,2) = 0.3340567% semester ; f(1,3) = 0.324776% semester ; f(1,4) = 0.329040% semester
f(1,5) = 0.306719% semester ; f(1,6) = 0.282498% semester ; f(1,7) = 0.217904% semester
f(1,8) = 0.2978% semester ; f(1,9) = 0.491202% semester
f(1,9) = (1.004434805^9/1.000625195)^(1/8) -1
These are the expected spot rates in 0.6958904 semesters, there is no forward rate for nine semesters. Estas son las tasas al contado esperadas en 0.6958904 semestres, no hay tasa futura para nueve semestres.
Swap rates or spreads. Tasa swap o márgenes diferenciales:
Given an 8 semester forward rate and an 8 semester spot rate. (0.491201 - 0.2683594)*100 = 22.28416 bps. Dada una tasa a futuro para 8 semestres y una tasa al contado para 8 semestres....
Sources/Fuentes: www.oup.com/us/ppt/derivatives/DMCH13.ppt (David Dubofsky & Thomas Miller)
-Finance By Kay Giesecke from Stanford University
-Financial Engineering & Risk Management By Martin Haugh & Garud Iyengar from Columbia University
