Recibido: 02-03-2021 / Revisado: 10-03-2021 /
Aceptado: 05-04-2021 / Publicado: 04-05-2021
Steadiness of expectation theory measured by swapt=
ion
curve
DOI: https://doi.=
org/10.33262/ap.v3i2.1.46
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image002.png")
La estabilidad de la teoría de la expectativa medida por la curva d=
e swaption
Antonio
Ruben Santillan Pashma. [1]=
Abstract
The
financial crisis that broke out in mid-2007 has spread in the existing
financial system with great instability favoring the devaluation of currenc=
ies
with the fall in market interest rates. This has caused potential investors=
to
become more risk-averse and therefore, look for financial products, although
lower profitability, also poses less risk. Following this line, it is the F=
ixed
Income assets that have acquired greater prominence in these times of
crisis. This article highlights t=
he
strength of the expectation theory in different tranches, using EURIBOR rat=
e to
determine implicit forwards, and estimate the price of a one-year swap cont=
ract
with 3 months of maturity,
and comparing in every moment with the real prices of swap as=
a benchmark.
SWAP is the bigger derivative inside of the group of Fixed Income Assets. <=
span
style=3D'mso-spacerun:yes'> After the quantitative analyst, it has =
been
observed how the theory prevails of sceneries of low volatility but falls on
sceneries when the volatility starts to increase. Introduction. One of =
the
basic assumptions about financial theory is talking about the expectations theory. Since the middle of the eighties,=
this
theory has been used as the unbiased estimator to calculate the swap intere=
st
rate in the base of the spot bank interest rate. Aim. Quantitativa analyst of the
steadiness of expectations theory in differents=
economical cycles, using the European Central bank as=
the
source to get hold of the EURIBOR spot rates for 3 months, 6 months, 9 mont=
hs,
and 12months from 2004 to 2016. Re=
sults.
During the periods before the crisis 2007, the prices of the IRSWAP are alm=
ost
adjusted between the market and what the financial theory says. The situati=
on
starts to change after the financial crisis when the volatility of the mark=
et
starts to increase due to the instability of the banking sector and traders
started with speculations strategies forgetting the aim of hedging, operati=
ng,
new positions the majority in the short term. Conclusion. Whether for speculative reason or interventions act=
ions
of the monetary authority, the theory e “EXPECTATIONS THEORY”, it is no=
t an
efficient predictor with out using a premium ri=
sk,
during the periods of high volatility.
Keywords:=
Swaps,
Quantitative Easing, Interest Rate, Forwards, Expectation Theory.
JEL codes: G120, G150, G170
Resumen
La crisis financiera que
estalló a mediados de 2007 se ha extendido en el sistema financiero existe=
nte
con gran inestabilidad favoreciendo la devaluación de las monedas con la c=
aída
de las tasas de interés de mercado. Esto ha provocado que los inversores
potenciales se vuelvan más reacios al riesgo y, por tanto, buscar productos
financieros, aunque de menor rentabilidad, también supone un menor riesgo.
Siguiendo esta línea, son los activos de Renta Fija los que han adquirido =
mayor
protagonismo en estos tiempos de crisis. Este artículo destaca la solidez =
de la
teoría de las expectativas en diferentes tramos, utilizando el tipo EURIBOR
para determinar forwards implícitos, y estimar el precio de un contrato sw=
ap a
un año con 3 meses de vencimiento, y comparándolo en cada momento con los
precios reales del swap como Un punto de referencia. SWAP es el derivado m=
s
grande dentro del grupo de Activos de Renta Fija. Después del analista
cuantitativo, se ha observado cómo prevalece la teoría de escenarios de b=
aja volatilidad pero cae en escenarios cuando la volatilid=
ad
comienza a aumentar. Introducción. Uno de los supuestos básicos de=
la
teoría financiera es hablar de la teoría de las expectativas. Desde media=
dos de
los años ochenta, esta teoría se ha utilizado como estimador imparcial pa=
ra
calcular la tasa de interés swap en base a la tasa de interés bancaria al
contado. Apuntar. Analista cuantitativa de la teoría de la estabilidad de =
las
expectativas en diferentes ciclos económicos, utilizando como fuente al Ba=
nco
Central Europeo para hacerse con los tipos spot EURIBOR a 3 meses, 6 meses,=
9
meses y 12 meses de 2004 a 2016. Resultados. Durante los períodos
previos a la crisis de 2007, los precios del IRSWAP casi se ajustan entre el
mercado y lo que dice la teoría financiera. La situación comienza a cambi=
ar
luego de la crisis financiera cuando la volatilidad del mercado comienza a
aumentar debido a la inestabilidad del sector bancario y los operadores
comenzaron con estrategias de especulación olvidando el objetivo de cubrir,
operar, nuevas posiciones la mayoría en el corto plazo. Conclusión=
. Ya
sea por motivos especulativos o por acciones de intervención de la autorid=
ad
monetaria, la teoría y la “TEORÍA DE LAS EXPECTATIVAS”, no es un pred=
ictor
eficiente sin utilizar una prima de riesgo, durante los períodos de alta
volatilidad.
Palabras clave: Swaps, flexibilización
cuantitativa, tasa de interés, forwards, teoría de la expectativa.
Códigos JEL: G120, G150, G170
Introduction
According
to the expectations theory and principles of non-arbitration, the interest =
rate
swap deliver by the mark has to provide the same performance as a single
investor who evaluates the derivate using forwards with spot interest rate
provided by the central bank, the volatility of the swaps depends on the
economic cycle, those products can be easy influenced not just but the powe=
rs
of the markets, the prices can also depend by the actions of the central ba=
nks
playing in the economy because in the majority of the cases they control the
supply of money.
That’s
one of the main reasons to be able to understand the changes of the curve,
investors have to study the volatility of the curve, Jacob Gyntelberg
and Christian Upper (2013) had made a complete analysis about the interest =
rate
swap market and how the market has been behaved before and after the 2007
crisis, it has demonstrated that SWAP shows positive turnover growth. The
analysis was developed for different currencies EU, USD, GBP, the main turn=
over
it continues in the developed markets, therefore, It
can be assumed that the volatility in those markers can be lower, but it ca=
n be
also the market it is not predictable in crisis time.
Juan
Ángel Lafuente, Nu=
ria Petit,
and Pedro Serrano (2015) analyzed the causes of the different prices of the
derivate because of the increasing of the risk premia, the article use a
vanilla SWAP to make the analyses since the crisis of 2007, providing the
biggest changes in the prices curve is due to a level factor capturing the =
90%
of the movements of the prices and increasing the volatility of the deposit
rate derivate is higher than deposit rate that it`s complementary to the
results of this paper, Johan Duyvesteyn and Gerben de =
Zwart
(2015), the analysis of the term structure risk premia in a base of the
building positions in the short and long term, shows that the volatility ri=
sk
premium is shorter within short positions the risk premia don’t affect the
model as in long term, the analysis has been made for four markets (USD, JP=
Y,
EUR, and GBP).
Those
paper and others that have been not mentioned, it supports the conclusion of
these research that about the Expectations Theory, that in time of high
volatile that the market increase the risk premia and that affect the valua=
tion
of the deposited rate derivate that is more volatile than the deposited rat=
e,
because of the conditions of the operations of the market the stocks market=
s can
change the positions faster than banking markets, affecting directly in the
prices of the SWAP. At the end of this article, it could be observed how the
financial theory will not prevail in face of unexpected circumstances on the
market, propitiating the unsteadiness of the forward as a predictor of the =
SWAP
prices.
Literature Review
Due to the increase of the turnover of=
the
fix income division and the instability of the market since the financial
crisis of 2007, the fix income has increased in last decades with the prese=
nce
of unusual fluctuations. This is the main reason why different publications
appeared related to this topic. One of those papers was published by Juan <=
span
class=3DSpellE>Ángel Lafuente, Nuria Pe=
tit and
Pedro Serrano (2015) analyzing the causes of the multi-curve framework using
basic SWAPs spreads –floating-to-floating interest rate SWAPs as an instr=
ument
for extracting the interest rate curve differentials. Together with Johan Duyvesteyn
and Gerben de Zwart (2015) they create an empir=
ical
analysis of the term structure in the volatility risk premium in the fixed =
income
market by constructing long-short combinations of two at-the-money straddles
for the four major swaption markets (USD, JPY, EUR and GBP).
One of the main strategies within the =
fix
income division is the SWAPS what will be analyzed in this dissertation. To=
the
analysis, the estimation and an understanding of these strategies is necess=
ary
to study the principals of the macroeconomic variable interest rates.
Therefore, authors as Fatma Chakroun, Fathi Abid (2014) has been referred to who writes abo=
ut
"A Methodology to Estimate the Interest Rate Yield Curve in Illiquid
Market: The Tunisian Case." As the title of the article says the main =
goal
if the authors was to create a methodology to es=
timate
the interest rate yield curve in an illiquid market like is the Tunisian bo=
nd
market, with the applied method of the cubic spline interpolation.
Furthermore they focused on the work of Vasicek from the year 1977 and of Cox-Ingersoll and R=
oss
from 1985, from where they got the prediction of the dynamics of the intere=
st
rate yield curve through the methods OLS (Ordinary Least squares) and the (=
MLE)
Maximum Likelihood Estimation. The authors concluded that if the Tunisian b=
ond
market does not have a yield curve, it is because it’s an illiquid market=
with
a very small trading quantity even if we are comparing it with other countr=
ies
that are also classified as developing nations, what it makes extremely
difficult to get an accurate interest rate yield curve. However
with the methodology that they used it was possible.
The results (empirical) shows that with
the using of the cubic spline method was the best solution for a market with
low level of trading, and it was possible to build an accurate average yield
curve that indicates that the spread between the long-term and the short-te=
rm
yields is pretty small what can cause a predictable high inflation. Finally,
they ensure that the methodology that they used can be very useful to create
the monetary policy for a country, and for the financial institutions it ca=
n be
very helpful in order to predict in trading activities the losses in the ca=
se
of disadvantageous movements of the interest rates.
In association with the findings of the
analyses of the interest rate is to be continued with =
Yacine
Ait Sahalia, Mustaf=
a Karaman, Loriano Mancini =
(2013)
describe in the article "The Term Structure of Variance Swaps and Risk
Premium" the analyses of the term structure of three components: varia=
nce
swaps, equity and variance risk premium. They compared the Variance Swaps and th=
e Volatility
Index, and they concluded that in the case of Variance Swaps there is an
important element: the time-varying jump risk.
Secondly based on their own model, they affirm that the term structu=
re
of variance risk premium can be characterized for being negative and normal=
ly
downward sloping what it has as a consequence that the short-end of term
structure shows the fear of the investors on a market crash, they are more
afraid of the impact of random volatility on the investment set.
In the case of the term structure of t=
he
equity risk premium, they defined it as countercyclical but with a procycli=
cal
slope. To conclude, the equity and variance risk premium term structures re=
act
almost evenly to current economic indicators. The aim of the authors Ravi B=
ansal,
Hao Zhou (2001), in their article
"Term Structure of Interest Rates with Regime Shifts" is to show
through a model how the regime shifts can affect the entire term structure =
of
interest rates, even when there are another works that prove that before th=
ese
term structure models with regime shifts were developed in 1997 by Nail and=
Lee
and in 1998 by Evans.
There is one important difference, bec=
ause
Bansal and Zhou studied how the regime shifts also affect the framework that
controls the market prices of risk. They conclude that the main goal of the=
ir
work is to prove that this is an efficient model because it takes into
consideration the regime shifts as a vital part for the conditional joint
dynamics of short and long yields and that there is a strong connection amo=
ng
the business cycles and regimes shifts. Continued with the capital prices J=
acob
Gyntelberg, Christian Upper (2013), had develop=
ed a
complete analysis about the interest rate swap market after the 2007 crisis,
finding a low but stable interest rate with low but positive turnover growt=
h.
The analysis was developed for different currencies (EUR, USD, GBP), in spi=
te
of the fast growing of different developing countries the main markets are
still situated in the oldest markets.
At the beginning of the article
, "The OTC interest rate derivate market in 2013", the aut=
hors
mention that in order to analyze the market for OTC (over-the-counter) inte=
rest
rate derivate they are using the data from the Triennial Central Bank Surve=
y.
In the first years of the 80s this market has grown enormously and during t=
he
1980's and at the middle of the 2000's was stable however in the last years=
has
suffered a lot of changes and the=
main
reason of that are the regulations in order to make a market more transpare=
nt
and decrease the counterparty risk. The
main changes have been the increasing share of transactions that at now
There is a positive side and a negativ=
e on
this. The positive is that this kind of new regulations will reduce the
counterparty risk and the negative side is that the over regulation will ma=
ke
in this market that the trading will cost more. Regarding the negative part
Robert N McCauley (1999) examined the effect of the introduction of the eur=
o on
the liquidity of European fixed income markets.
Interest Rate =
SWAP
The temporary interest rate structure, as a relationship between the
different interest rates existing in a market, and depends on the term in w=
hich
they are applied, daily, monthly, annual, etc. A continuous term structure
could be observed directly from the public debt market for each asset with
zero-coupon security without credit risk. However, only a finite number of
titles are available in the market. The usual list is 3 months/period, 6
months/period, 1 year/period in short term, and bonds of 10 years/period and
their prices are defined for a finite number of points that the analyst can=
use
to build a temporal yield (pag16, we can observe the curve).
Most of the titles that are on the market pay coupons periodically, =
the
credit quality of these bonds depends on the risk market, liquidity, and ot=
her
factors that can affect directly or indirectly the value of the asset on the
market (John C Hull, 2005). How has been defined the credit quality of the
title depends on the market where the title is operated. Thus, traders and
analysts use the prices of the titles of countries that are considered secu=
re,
due to the low inflation, standard growth, low level of debt to estimate the
prices of their public debt assuming that the titles from countries are not
exposed to credit risk. In the eurozone, it is used the prices of the German
bond (Mario Bajo Traver and Emilio Rodríguez Alfonso, =
2005)as
a reference price of titles free of insolvency risk.
In Figure 4, It can be observed how sovereign bonds are the zero risk
bonds, pay a very low-interest rate but are assets free risk, while corpora=
te
bonds are normally rated by different risk agencies (Standard & Poor's,
Fitch Group, Moody’s), are bonds with a higher level of probability of de=
fault
but the yield that could generate is higher to the holder in case of payment
compliance.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image004.png")
Source: LIBOR 2015.
Figure 1 Term structure rate by Credit Risk
Within the fixed income market there are different types of interest
rate curves, spot, forward, SWAP (Eliseo Navarro and Juan Nave, 2001).) but=
the
most significant on the market is the spot or cash curve. The spot curve ca=
n be
estimated by observing the daily interest rate on market, although; it is
relatively easy to estimate one curve using another. There are different
analytics possibilities to estimate the term structure of the interest rate=
s,
using discreet models or continuous models (Vasicek, Svensson, Cox-Ingersoll, and Ross).
However, it is necessary to provide an introduction of the interest =
rate
yields; there are different authors which can get the readers into a deep of
knowledge of how to estimate the different curves, for example, Fatma Chakroun and Fathi Abid 2=
014), as
it was mentioned before using continues models (Vasice=
k
1977), and Cox-Ingersoll and Ross=
CIR
1985)). It is not the purpose of this dissertation to analyze the yields, e=
ven
though, It is going to be mentioned in the follo=
wing
sections a brief explanation of basic terminology necessary to understand t=
he
operationally of the markets and the movements of the interest rates. Model=
ing
of the different curves is carried out by the monetary authority of each
country, central banks. It should be noted, the estimation of the term
structure of interest rate depends to a great extent on the results and the
reasons why the one being modeled and although in all cases the results are
similar, it cannot be said that there isn’t a uniform estimation. For our
analysis, we will use the (Svensson 1994) model to investigate the behavior=
of
various curves of interest rates after having analyzed the volatility of the
price of the Swaps and understand how the market has behaved at each moment=
.
Depending on the market and the moment, it can be observed different
types of curves and each of them depends on the risk of involvement and an =
inversely
proportional relationship can be observed with a higher risk of insolvency,
lower credit quality and therefore the bond offerors will have to pay a hig=
her
interest rate to make your asset more attractive to investors (Ravi Bansal =
and
Hao Zhou, 2001). It should be not=
ed that
depending on each case, the term structure of interest rates can take diffe=
rent
forms, thus a flat structure can be appreciated, which informs us that the
interest rate is unique for any type of maturity. A decreasing structure wh=
en
short-term interest rates are higher than long-term interest rates (eurozone
crisis 2012), a growing structure that the most common, the time value of m=
oney
plays an important role and therefore the interest rates to short-term rates
are lower than long-term rates
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image006.png")
Source: LIBOR 2015.
Figure 2 Term structure of interest rates
For a=
nother
hand, to estimate a Term Structure of interest rates (TSIR for now on), it =
is
necessary to know which it is the returns of the financial assets that oper=
ate
on the market, understanding the yield as the average rate of return that an
investor will receive, if they held the asset until the maturity of the
operation. The valuation of a bond in the market is given by the following
expression (Eliseo Navarro and Juan Nave, 2001):
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image008.png")
Equation 1
M=3D
value at maturity
c
=3D coupon
i=3D interest rate
n=3D
number of payments
Where the price p of the bond is in the function of the periodical
payments expressed as a coupon c, the required interest for assuming certain
risk i, and the number of payments that the own=
er of
the bond will receive n. The pric=
es of
the bonds can build a TSIR finding different bonds with different maturities
and similar risk as it was commented the governments are the most popular
instruments to build a TSIR. Depending on the term of the bond, the level of
profitability required changes, in the long term the yields are higher, whi=
le
in the short term the yields are lower because of liquidity premiums.
Fixed income markets depend on the type of assets that are traded on
them, it can be distinguished as money markets (with debt at short term and
little risk or high liquidity) and capital market (to negotiate debt with
medium and long-term maturity). These are the most important and necessary
segments of the market where the financial analyst operates with interest
rates. In these circumstances, spot and forward rates acquire greater
importance. It can be denominated as spot rate to the discount rate at the
current time. Spot interest rates=
can be
observed in the wholesale market where only, credit institutions are involv=
ed.
It allows, among others, to establish the price of money through the loans =
that
financial institutions make between them (generally in terms of one day or =
one
week). In the eurozone is where basically according to intraday operations =
the
financial authority European Central Bank sets the spot rate, named EURIBOR
rate as the average of the rate with which eurozone banks carry out commerc=
ial
exchanges. If the financial operation is executed in the future the expected
discount rate at a future time of the asset is demonized forward rate (Elis=
eo
Navarro and Juan Nave, 2001).
In Figure 3 it can be observed the financial operation in t=3Do with=
the
knowing interest rates and another operation traded in t=3D0 with an unknow=
ing
discount factor that will be done in t=3D1 with the expected interest rate =
based
on the interest that is today.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image010.jpg")
Source: John C Hull, 2005.
Figure 3 Forward Expression
The r=
elation
between spot rate and forward rate can be expressed with the following
equation, where Let toRt1
and toRt2 be the current spot rates at t0 =
for
the periods <=
!--[if gte msEquation 12]> Equation 2 Where: Note that the forward rate is the one-year spot interest rate that
should be valid within one year so that the result of the two-year investme=
nt
produces the same result as investing successively at one year and reinvest=
the
result for one more year. A very important property and where this analysis=
is
focused is that forward rates, so that there are no arbitrage opportunities,
should coincide with future rates but If the interest rate estimators are n=
ot
unbiased, we see that there are arbitrage opportunities (Eliseo Navarro and
Juan Nave, 2001). Intuitively, the forward interest rate corresponding to a certain te=
rm Source: Eliseo Navarro and Juan Nave, 2001 Figure
4 Forward Relation To avoid the risk of reinvestment financial enti=
ties
use “zero-coupon rates” to value monetary flows and calculate these int=
erest
rates that provide the implicit rates. These interest rates are not obtaine=
d in
the financial market, since they do not exist for long-term time horizons, =
so
it is necessary to start from the price of other highly liquid assets
(government bonds, interbank rates, swaps, etc.), with different maturities.
One of the possibilities to estimate the zero-coupon yield is using models =
as Vasicek y Fong (1982), Modelo de
Nelson y Siegel (1987), and the Svensson (1994) model. The interest rate that of any financial asset as a bond, FRA or SWAPs
pays always moves against its performance. This is logical if we understand=
the
price of the asset as a function directly related to the periodic payments =
that
the owner of the SWAP (one of the most common assets in the financial marke=
t)
has the right to receive. If we believe that interest rates are going to fa=
ll,
older SWAPs (and therefore that are offering higher coupons than expected) =
will
have more value. Conversely, if we believe that market interest rates are g=
oing
to rise, old SWAPs will lose value (as they will be offering lower payments
than new issues are expected to do). With the generation of the MATLAB code. This article discusses the
relevance of the financial theory during the time or changes in the curve of
the interest rate due to causes beyond the normal operation of market, Juan=
Ángel Lafuente, Nuria Pe=
tit, and
Pedro Serrano (2015) have proved that the difference of the swap prices is =
due
to the volatility of the risk premium proving that the valuation of the
derivate is highest sensitive to the conditions of the markets, based on th=
is
the results of this research confirm that the financial theory does not pre=
vail
in times of extreme volatility because the theory of expectations it is not
consistent, forwards are not unbiased estimators of the future spot rates.
Affectation the following hypothesis the analysis has begun: Forwards are n=
ot
good predictors of the swap rate, under cases of high volatility – “The=
ory of
expectations does not prevail”, banking market is less volatile than the =
stock
market, hedging strategies change by speculative strategies increasing the
volatile of the market. In a conjunctural moment like the present, in which
there has been a strong financial crisis caused by the COVID-19 pandemic,
economic agents will begin to see swap products as allies in managing the r=
isks
of their economic activity, only to the extent that the benefits are fully =
understood
and the risks inherent in these structures, their scope, and limitations. Focusing on a quantitative approach using the European Central bank =
as
the source to get hold of the EURIBOR spot rates for 3 months, 6 months, 9
months, and 12months from 2004 to 2016. The interest rate database will be
depurated confronting the swap prices that will be mentioned after, to
eliminate from database those days without transaction in the market, where
either will be interest rate but will not be swap price or will be swap pri=
ce
but not the interest rate. Exclud=
ing for
this analysis the not trading days because of the weekend, holidays
indeterminate market or days off of the main actors of the market due to un=
expected
events such as the stoppage of the transaction by government order, for exa=
mple
in the middle of 2007. Source: European Central Bank Figure
5 EURIBOR from
2004 to 20016 Once the term structure of interest rate has obtained with different
maturities as 1 month, 6 months, 1 year, 2 years 5 years, and 10 years ( the
most common points on the yield), the equivalence equation will be=
used
to calculate will continue with the extrapolation of the forward's rates us=
ing
the equation number two mentioned before on this dissertation. The equation
will allow the research to use the spot rates to calculate the forward's ra=
tes
as part of the financial theory, where spot rates are unbiased estimators of
the forward's rate using the theory of expectations (John C Hull, 2005). The theory of expectation affirms that a spot rate contains informat=
ion
of the expectations of the investors about the spot rates that governments =
will
use in the future (Lutz, 1940), the expectation theory was developed based =
on
excessively restrictive hypotheses, the theory has the idea that economic
activity takes place in an environment of absolute certainty, and there is =
not
asymmetric information between counterparties and that fixed income securit=
ies
with different maturities are perfect substitutes, for example, investing i=
n a
two-year zero-coupon bond is equivalent to Invest in a one-year non-coupon =
bond
and renew that investment again. This theory will be disputed based on the
results of this dissertation. To demonstrate the weekends of the expectation theory, It is going t=
o be
compared as a benchmark the price of three months interest rate swap one ye=
ar
of maturity (SWAP3m1Y ) from 2004 to 2016 (SWAP prices rates will be obtain=
ed
in Blomberg which is made in the market with their intraday operations), wi=
th
the estimation of the prices that will come using forwards rate and fitting
those rates into the equation three (John C Hull, 2005). How it was mentioned and develops in chapter one of this dissertatio=
n,
the swap is a contract that allows the transactions of cash-flow with not
capital movements; the derivate permits two counterparts to exchange cash-f=
lows
originating by loans or in some cases for investments. The most common SWAP=
is
the plain vanilla, where one of the counterparts assumes a fixed position or
fixed leg where they have to pay a fixed interest rate and the other
counterpart assumes the floating position or floating leg having to pay a
floating interest rate. At this point, it has to clarify that the notional of the contract
always remains constant, and the only payments which are transferring betwe=
en
the counterparts are the deference the amount of money that it has to payme=
nts
for the fixed leg and the amount of money that the floating leg has to
pay. <=
span
lang=3DEN-GB style=3D'font-size:12.0pt;font-family:"Cambria",serif;mso-fare=
ast-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";mso-ansi-language:
EN-GB;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'> <=
span
lang=3DEN-GB style=3D'font-size:12.0pt;font-family:"Cambria",serif;mso-fare=
ast-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";mso-ansi-language:
EN-GB;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image012.png")
and <=
/span>![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image014.png")
. Then, It can define the implicit inter=
est
rate or forward in t0 that belongs to the term ![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image016.png")
that
fulfills the following expression: t0 F t1,t2
(t0 < t1 < t2 ),
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image018.png")
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image020.png")
=3D S=
pot
Interest from t0 to t2![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image022.png")
=3D S=
pot
Interest from t0 to t1![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image028.png")
=3D F=
orward
Interest from t0 to t1 t2![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image030.png")
is nothing more than the spot interest =
rate
that should be in effect at t1, so that the result of an investment in the =
term
generates the same result as investin=
g in the
term and reinvesting the resulting amount in=
a
second operation at an extended-term t2- t1.![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image032.jpg")
Methodology and Data
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image034.png")
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image036.png")
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image038.png")
Interest
Rate SWAP
Equation 3
Where:
M: Ca=
pital
with which the contract is opened.
Ft:
Df:
Discount factor for the ti period.
Once the valuation of the swap will be completed and with the
expectation of a better understanding of the situation what is happening wi=
th
the swap prices and with the European economy. It will analyze the prices
dividing the time series into different parts one part will be from 2004 to
2005 when the conditions of the market were stable, the second part will st=
art
with the financial crisis of 2007 and the fall of Lehman Brothers, the third
will be once the bank nationalizations started in united states, the fourth
part will focus when the market starts the attack against the euro and it w=
ill
end with the applications of quantitative easing policies in the eurozone. =
In
order to provide a better explanation, it is going to be necessary to estim=
ate
the yield curve for each scenery, intending to use the TSIR theory to have a
better explanation of what happened in the market.
The estimation of the yield curve will be developed using the Svenss=
on
model 1994, the model proposes to estimate the parameters of the zero-coupon
curve minimizing an adjustment measure such as the sum of squares of the er=
ror
on spot prices. The estimation is carried out employing maximum likelihood,
non-linear least squares, or the generalized moment method.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image040.png")
Svens=
son
Model (1994)
Equation 4
Where:
It
has to estimate six parameters via a least-squares or similar algorithm: β=
1,
β2, β3, and,. For m observed yields with diffe=
rent
maturities τ1, . . . , τm=
.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image042.png")
The
formula of Svensson will be used in this dissertation to compare the differ=
ent
changes in the slope of the curve of the interest rate in different economic
circumstances, which will be important to understand the consequences of the
contraction and growth.
Results
Consi=
dering
that Bloomberg provided the stock market prices of SWAP with real operations
prices, has been compared the estimation made with the forwards using EURIB=
OR
rates (Figure 6), it can be observed the time series of swap prices that are
negotiated on the market from 2004 to 2016 coming from Bloomberg (blue line)
that it is performing as be the benchmark of the estimate swap prices as a
result of the estimation of this dissertation (red line). During the periods
before the crisis 2007, the prices of the IRSWAP are almost adjusted between
the market and what the financial theory says about forwards that are unbia=
sed
estimators of the prices of the future rate for that reason the predictions
made in this dissertation coincide with the real prices using by traders to
operate into the stock market.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image044.jpg")
Source:
Based on Matlab Simulations
Figure.6
Economic Singularities on the market.
The situation starts to change after the financial crisis when the
volatility of the market starts to increase due to the instability of the
banking sector and traders started with speculations strategies forgetting =
the
aim of hedging, operating, new positions the majority in the short term with
the objective of increase their performance started to concentrate the majo=
rity
of the transactions increasing the volume of turnover. Jacob Gyntelberg<=
/span>
and Christian Upper (2013) had explained that the volume of turnover has
increased in the last 10 years using IRSWAP and one of the reasons that cou=
ld
explain why it has increased is because the volatility of the market has
attracted to concentrate investment of speculative investors in this produc=
t.
However, to not go from our hypothesis we can distinguish two differ=
ent
scenarios, the first is when the risk premium does not affect the valuation=
of
the IRSWAP and the theory of expectations prevail, and the second scenery w=
hen
the financial theory falls and the risk premium affects the valuations of t=
his
derivate as was mentioned (Juan Ángel Lafuente, Nuria Petit and Pedro Serrano 2015), observ=
ed
Figure 7, where it can divide the time series into 5 parts first before of
2007, second part Bank Nationaliz=
ation
USA and EURO Crisis 2009 and finally Financial Market bet against of EURO 2=
012, in the last part with the Quantitive
Easing Policies the volatility of the market has been reduced and the
differences between prices are not significant.
Analysis of Different Sceneries
Before Subprime Mortgage Crisis 2007
Stable
economic environment stable, the negative slope of the curve, a strong
initiative to short-term investments, not a dynamic market, low volatility.=
The
estimated yield curve matches with the prices of the market. The prices of =
the
swap were stable from 2004 to 2005 due that the volume of negotiation of th=
is
product in the market was not popular and the stable conditions of the mark=
et
with any didn’t disruptive elements that can affect the negotiations and =
the
interest rate it is noted that the real prices are almost equal than the
estimated prices. It can be confirmed that expectation theory prevails and =
spot
rates are transferring information to the investors about the future prices=
of
the swap. Spot rates are unbiased
estimators of the forwards and forwards are unbiased estimators of swap pri=
ce
the aversion of risk of the market agents is stable.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image046.png")
Source:
Based on Matlab Simulation
Figure
7 Before Subprime Mortgage Crisis 2007
Accor=
ding
to financial theory, the appearance of curves with negative slope is a sign=
al
of the changes in cycles of the economy and anticipated recession are comin=
g to
the economy.
Financial Cris=
is
and Lehman Brothers collapse 2008
Uncer=
tainty
in the market, increased interest rates, increased market Volatility. After=
the
crisis of 2007 and with the fall of Lehman Brothers in the United States the
prices of the swap have fallen in both time series and it begins to see a
difference between the prices traded on the market and the estimation price=
s.
Due to that conditions of the market has changed and there are more instabi=
lity
and unknowing conditions of the future the government and investors have the
idea that unexpected events will come and the spot rates can’t provide ac=
curate
information to the model and the predictions are not exact but even though =
the
with the information that is in the market the estimation doesn’t much in=
exact.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image048.png")
Source: Based on Matlab Simulation
Figure 8 Differences in the prices of SWAP.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image050.png")
Source: Based on Matlab
Simulation
Figure 9 Financial Crisis and Lehman Brothers coll=
apse
2008.
Bank Nationalization EE.UU
and Euro Crisis 2009
Drast=
ic
fall in interest rates bank panic. Central banks try to maintain the level =
of monetary
circulation, rates are at historic lows. As a consequence of the changes in=
the
market, the slope of the curve remains positive following the economic theo=
ry
about risk aversion, which says agents are not expected big changes in the
short term that is the reason that risk of the asset is low and lower return
and investor has to receive more returns for assets in long term.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image052.png")
Source:
Based on Matlab Simulation
Figure
10 Bank Nationalization EE.UU and Euro Crisis 20=
09.
Euro Crisis
The f=
inancial
market bet against the euro, the sovereign debt crisis, the banking system,=
and
the economic system in general. I=
n 2012
markets start to bed against the euro and the eurozone increasing the idea =
the
unexpected circumstances will come to the market increasing the volatility =
of
the swap prices. That is why spot rates can’t transfer accurate informati=
on to
the forwards and the model is not able to estimate the correct swap prices =
as
can be observed in Figure number 24, at this point of this dissertation it =
can
be concluded that one of our hypotheses has been contrasted, the theory of
expectations doesn’t prevail under increases of volatility in the market =
and
spot rates are not unbiased estimators of the forwards.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image054.png")
Source:
Based on Matlab Simulation
Figure
11 Differences in the prices of SWAP in percentages.
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image056.png")
Source:
Based on Matlab Simulation
Figure
12 Euro Crisis
2012.
Quantitative
Easing - EU 2015
The
European central bank intervenes in the economy, with massive purchases of
public and private debt valued at about 60,000 million per month until at l=
east
September 2016. The massive purchase of debt stabilized the market prices a=
nd
transferred stability to the market reducing the discrepancies between the
observed prices and the estimated prices, providing to the spot rates more
information to generate better estimations but it is not sufficient to come
back to normal activity before the crisis of 2007 where the prices were
accurate to the observed in the market. =
![](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image058.png")
Source:
Based on Matlab Simulation
Figure
13 Quantitative Easing - EU 2015.
Discussion and Conclusion
In this research we can appreciate that
volatility is one of the major parameters to take into consideration to
evaluate any derivate, basically, the theory of expectations which affirms =
that
forward rate is an unbiased estimator of the future spot interest rate, are=
not
consistent during volatility periods this is one of the biggest results tha=
t we
can observe with the modeling of our data, being consistent with
Whether
for speculative reason or interventions actions of the monetary authority,
shifting the interest curves to other levels unpredictable for the market
analyst, but the
financial theory especially “EXPECTATIONS THEORY”, not come to meet and=
forward
as a forecasting tool to become inefficient predictor with our using of the premium
risk, during those periods to correct differences between models being the =
main
aim to make real predictions using another econometric tool like Montecarlo Simulation, to advice traders when they ha=
ve to
correct the positions.
The monetary market is more volatile t=
han the
stock market, one of the main reasons why SWAP financial products have emer=
ged
is undoubtedly the limitation found in other derivatives such as futures,
options, which are derivate negotiable within exchanged markets. SWAP as a
forward has the peculiarity of being an open instrument, where the partners=
are
free to negotiate the terms of the contract, such as the interest rate to be
applied, the maturity of the contract, the amounts of negotiation, periodic=
ity
payments, among others and significant advantage using SWAPs the capital ne=
ver
exchanged just exchange interest rates cash-flows.
Thus, an investor willing to extend the
performance of his portfolio, and consider that interest rates do not behave
logically and will be reduced in the future, by the application of monetary
adjustment policies from banks central (quantitative easing), a trader may
enter an IRSWAP with a variable position, which certainly can get to beat t=
he
market performance, because the market expects that the interest in the fut=
ure
has to be higher than the current interest rate.
Traders in that case then have to gene=
rate
new expectations about interest rates, and those new expectations can move =
Term
Structure Of Interest Rates (TSIR), makes reduce=
the
interest rate with those movements the traders can positioned in long (buy)=
or
short (sell) according to with the new expectations of the curve. Once the
trader has determinate the new expectations of the curve the interest rate,=
he
has to develop new strategies which allow managed a portfolio with a better
profile than the profit of the market.
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Para citar el artículo indexado
Santi=
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measured by swaption curve . AlfaPublicaciones, 3(2.1), 6–26. https://doi.org/10.33262/ap.=
v3i2.1.46
![3Deditorial1.png](3D"1.STEADINESSOFFINANTIAL_AntonioSantillanFinal_archivos/image061.jpg")
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