Friday, October 26, 2012


Calculadora para Callable Bonds

Con esta calculadora, usando un modelo binomial simple para simular la short rate, ustedes podrán calcular el precio de un Callable Bonds y consecuentemente de la opción incorporada en el mismo. Asmismo, también se puede observar en un gráfico la sensibilidad del precio del Callable Bond ante cambios en la short rate.

Thursday, October 11, 2012

Aclarar no siempre oscurece


El 16/07/2010 el Banco Central de la República Argentina (BCRA) mediante la Comunicación “A” 5099, luego reemplazada por la Comunicación "A" 5265, estableció nuevas normas aplicables a la cancelación de deudas financieras externas de gobiernos locales por préstamos de no residentes y emisiones externas de bonos y otro títulos de deuda. Principalmente dando definiciones más precisas respecto a Gobiernos Locales y Deuda Externa.

En particular, se define como 
  1. Gobiernos Locales: comprende la administración central de provincias, de la Ciudad Autónoma de Buenos Aires, y de las municipalidades del país.
  2. Deudas financieras con el exterior: deudas contraídas con no residentes que no tengan su origen en una operación de comercio exterior argentino, o que teniendo este origen, no califican en la normativa cambiaria como una deuda comercial con el exterior.
  3. Bonos y otros títulos de deuda externos: bonos o títulos emitidos en el exterior que cumplen con las siguientes condiciones:
    • la emisión se efectúa en el extranjero acorde a las reglamentaciones del país de emisión y se rige por ley extranjera,
    • es ofrecida y suscripta en su mayor parte en el exterior, para lo cual la emisión debe dar cumplimiento a las reglamentaciones del país de suscripción,
    • es integrada en su totalidad en el exterior,
    • los servicios de capital y renta son pagaderos en el exterior.
Es decir, en primer lugar dicha Comunicación no alcanza al Gobierno Nacional, el cual no está alcanzado por la normativa cambiaria tanto para los egresos como para los ingresos, y en segundo lugar, un título de deuda para ser considerado externo, es decir para que el emisor pueda acceder al Mercado Úúnico y Libre de Cambios (MULC) para su cancelación, no sólo debe haber sido emitido bajo legislación extranjera sino que también debe cumplir todos los requisitos enumerados previamente.

La primer pregunta a realizarse, y la más evidente, es, ¿Por qué el servicio financiero 66 correspondiente a amortización e interés del día 04/10/2012 fue el primero en ser abonado en pesos argentinos por el Gobierno del Chaco, dado que la Comunicación que colocó restricciones a Gobiernos Locales para el pago de títulos de deuda bajo legislación local (entre otros requisitos) data de mediados de 2010?

Es cierto que, dadas las condiciones del bono, el Gobierno del Chaco no tenía acceso al MULC bajo el concepto de pago de deuda externa[1] para hacerse de los dólares que le permitieran pagar el vencimiento de estos bonos, sin embargo podía comprar dólares bajo el concepto de Formación de Activos de Libre Disponibilidad (FALD), el cual tenía un límite mensual de 2 millones de dólares estadounidenses.

Sin embargo, la FALD fue suspendida mediante la Comunicación “A” 5318 con vigencia a partir del 06/07/2012. Con lo cual surge la segunda pregunta, ¿Cómo hizo el Gobierno del Chaco para abonar los servicios financieros 64 y 65 correspondientes a los meses Agosto y Septiembre, ya que no era posible acceder al MULC bajo ninguno de los 2 conceptos, es decir pago de deuda ni FALD?

En referencia a la última pregunta, la única alternativa viable sería que el Gobierno del Chaco haya, previo a las restricciones, adquirido los dólares mediante la FALD y los haya aplicado al pago de los servicios correspondientes, quedándose en este último mes sin disponibilidades para hacer frente a los vencimientos sucesivos, y viéndose obligado a enfrentarlos en moneda nacional.

Por otro lado, cabe destacar que la imposibilidad de acceder al MULC para el pago de deuda externa, ya sea por préstamos o títulos de deuda, alcanza únicamente a los instrumentos que no cumplan con las definiciones especificadas en la Comunicación “A” 5265. En consecuencia, parecería que el mercado ha sobre reaccionado respecto al evento ocurrido el martes pasado (09/10/12), vendiendo todo tipo de bonos denominados en moneda extranjera y no sólo los afectados por los cambios normativos, que cabe destacar están vigentes desde hace más de 2 meses.

A continuación presentamos las variaciones en los precios de una serie de bonos, por ejemplo los emitidos por el Gobierno Nacional (RA13, RO15, AA17), los cuales no se vieron afectados por la normativa cambiaria ya que el mismo no tiene restricciones de acceso al MULC. A pesar de ello, dichos bonos mostraron caídas entre 1.5% y 4%, incluso mayores a la observada en el bono emitido por el Gobierno del Chaco.


Situación similar presentan los bonos Discount de la provincia de Buenos Aires, que a pesar de ser un gobierno local, cumplen con todos los requisitos de deuda externa y por consiguiente tienen acceso al MULC para su cancelación.

Finalmente, el caso más emblemático son los cupones atados al PBI (TVPY y TVPA), cuya única diferencia es la legislación bajo la cual se encuentran emitidos, siendo el TVPY emitido bajo legislación de Nueva York y el TVPA bajo legislación Argentina.

Asimismo, como vimos en la normativa cambiaria, al ser deuda emitida por el Gobierno Nacional, no existen restricciones en materia cambiaria para su cancelación sin importar la ley bajo la cual fueron emitidas. Sin embargo, el cupón emitido bajo legislación Argentina mostró una caída de alrededor de 5 puntos porcentuales mayor que su par de Nueva York, sin que se observen factores que lo justifiquen[2]

En conclusión, en este trabajo, luego de evaluar la normativa cambiaria vigente, presentamos un claro ejemplo de cómo en ciertas situaciones los agentes del mercado financiero reaccionan ante un evento en particular, en este caso el pago en pesos del bono emitido por el Gobierno del Chaco, sin evaluar los alcances reales de dicho evento en el resto de los activos, en este caso los bonos del Gobierno Nacional, generando oportunidades de arbitraje para los agentes mejor informados.




[1] Para consultar los diferentes código de conceptos del MULC ingrese Aquí
[2] Cabe destacar que se encuentran expuestos al riesgo de futuros cambios en la normativa, riesgo al cual también se encontraban expuestos en el pasado, pero posiblemente percibido como más probable luego del evento en cuestión. Sin embargo, en caso que la normativa cambiaria comience a afectar al Gobierno Nacional, esto implicaría el default instantáneo del instrumento y con ello de todos los pasivos del Gobierno Nacional debido a la cláusula de Cross Default incluída en la mayor parte de ellos.

Thursday, October 4, 2012


Calculadora para Barrier Options

Con esta calculadora, que utiliza el modelo binomial, ustedes podrán calcular precios de Opciones de todo tipo, Call/Put, European/American, Down/Up, Out/In. Incluso si lo desean también pueden calcular precios de opciones con Rebate. Asmismo, también pueden utilizarla para observar la sensibilidad del precio respecto a las distintas variables.




Friday, September 28, 2012


Calculando el Blue Spread

A pesar que esta información se puede obtener mediante el tipo de cambio implícito en el contado con liquidación, me pareció interesante este mecanismo debido a exponer un ejemplo sobre como obtener información implícita en el mercado de bonos y asimismo nos permite observar si existen oportunidades de arbitraje entre los distintos bonos.

Son de conocimiento público las restricciones impuestas por el Banco Central de la República Argentina (BCRA) para la formación de activos externos de libre disponibilidad, es decir la compra de moneda extranjera sin fines específicos.

Dichas restricciones generaron distorsiones en los precios de los bonos denominados en moneda extranjera, a punto tal que los precios de muchos de estos bonos implican tasas internas de retorno (TIR) negativas, reflejando que los inversores están dispuestos a pagar un spread para percibir dólares billetes por medio de la compra de bonos, ya sea manteniéndolos hasta el vencimiento de los mismos o mediante otros mecanismos que exceden el objetivo de este trabajo.

La idea de este trabajo es extraer el spread implícito en los precios que los inversores están dispuestos a pagar en el mercado de bonos para hacerse de los dólares billete que no pueden adquirir en el mercado cambiario. Dicho spread será denominado “blue spread”.

Definiremos al blue spread como la diferencia entre el precio de mercado del bono y el precio teórico del mismo. Para calcular el precio teórico de los bonos utilizaremos la USD LIBOR, como una aproximación de la tasa libre de riesgo en dólares estadounidenses, y el valor de los Credit Default Swaps (CDS), como aproximación del riesgo de default del país, obteniendo a partir de estos dos valores la tasa de descuento asociada al riesgo Argentino .

Entonces el precio teórico del bono va a estar dado por,

donde “c” representa los cupones, “N” el nocional, “ri” la tasa spot libre de riesgo y “CDSi” el valor del CDS argentino con maturity i.

En particular para el cálculo utilizaremos el BONAR VII (AS13), que es un bono emitido por el Gobierno Nacional denominado en dólares estadounidenses, con vencimiento 12/09/2013, pago semestral de tasa fija al 7% y amortización al final.

El precio de mercado para invertir US$ 100 de valor nominal en dicho bono al 12/09/2012 era de $632 o al tipo de cambio oficial US$ 135.59 , implicando una TIR negativa de 21.44%, mientras que el precio teórico de este bono invirtiendo US$ 100 de valor nominal está dado por,

implicando un blue spread de US$ 36.72 o 37%.

De esta manera utilizamos la información que nos otorga el mercado de bonos para obtener información implícita en sus precios, en este caso para calcular el blue spread. Cabe destacar que el BONAR VII no es el único bono denominado en dólares del Gobierno Nacional, en consecuencia se podría utilizar el mismo mecanismo para obtener el blue spread a partir de los distintos bonos y determinar si los mismos respetan la condición de arbitraje.


Tuesday, September 4, 2012

Calculadora para estrategia con opciones

Les presento una calculadora para armar estrategias con opciones, básicamente yo la usé para evaluar una estrategia para explotar discrepancias en Skew de diferentes índices, pero puede ser utilizada para evaluar cualquier estrategia.

Espero que les sea de utilidad y compartan conmigo su experiencia usándola.

Tuesday, August 14, 2012

¿Hay cuerda para más política monetaria?

Es la pregunta que me hice cuando empecé a escribir este artículo y decidí titularlo así. 
Le agradezco a Germán Fermo por publicarlo en su blog y hacer de conexión para su publicación en Serenity Markets.

Les dejo los links para que elijan en que página les gustaría leerlo, y como diría Germán....ENJOY FINANCE


Wednesday, August 8, 2012

Implied Volatility and Voltaility Skew in Equity Index

spanish version

This time, the idea is to take a look at the volatility implied in the options and the volatility skew of different Indices around the world.

In the following table we can see the volatility implied in the one month maturity options, this mean the market expectation about the next month volatility of the different Indices. So, as we can see, the Indices perceived by the market as the highest volatile during the next month were Russia and Italy, both with an Implied Volatility greater than 30 points.

Furthermore, Italy showed a historically high volatility level (76%-ile[1]) with an increase of 20% from the previous month (5.7 volatility points). Same behavior showed all the Euro Area Indices with an average increase of 5.5 v.p., denoting an increase in the risk perception of this area in general.

On the other hand, Switzerland was the Index perceived as the less volatile for the next month and despite its volatility increase from the last month, it was in historically low levels (15%-ile). On overall, the perception of volatility in the equity markets increase in 2.1 v.p. since the previous month.

Options Volatility Screener

Another important variable to take a look at, in order to have a complete understanding about volatility, is the skew, defined here as the difference between the 25 delta implied volatility (IV) in puts and calls options normalized by the 50 delta IV. So the higher this value the more expensive, in terms of the Black-Scholes model, the puts are over the calls.

We can think about the skew as a measure of:

- Risk aversion: as the skew increase, the market players are hedging more positions by buying OTM puts and selling OTM calls, so the participants are becoming more risk averted.

- Relative tail events probability: as the skew become higher, the investors are paying more for OTM puts than for OTM calls meaning that their perception about the probability of a negative tail event relative to the positive one is more likely.

So we can think that changes in the Skew denoted changes in the risk aversion of the market players and changes in their perception about tail risk probabilities.

In particular, the Canada Index and the S&P 500 are the ones that show the bigger Skew in their options volatility. However, the Indices that are more skewed relative to the last four years were the Nasdaq and the Kospi 200, close to the 65%-ile. On the other hand, it is interesting to remark that most of the European Indices showed their Skew below the 10%-ile, values that look contradictory with the actual situation of Europe.

However, if we take a look at the evolution of these values, we find out that on average these countries reduce its skew about 50% (0.07 skew points) in the last month. One possible posible explanation of that could be the announcement of the ECB’s president Mario Draghi, saying that the ECB is going to make whatever it takes to preserve the euro. This means that the ECB is going to be there if a negative tail event would happen, reducing the probability of a negative tail event and with it the volatility skew.

In this direction, we are going to take a look at the evolution of the S&P 500 and the EuroStoxx 50 Skew, in order to see their reaction against the Monetary Easing announcements. As we can see, after each announcement both Skews show a reduction in their value. This makes sense because if you know that the FED or the ECB are injecting liquidity or purchasing assets, the negative tail event become less probable and the risk aversion goes down, producing a reduction in the skew.

Skew evolution and Monetary Easing

Another interesting thing we can see in the previous graph is that the correlation between the S&P 500 and EuroStoxx 50 was almost 80% in the last 4 years. However, in the last months these values separate from each other, with the EuroStoxx 50 Skew in the 5%-ile and the S&P 500 above the 50%-ile.

Based on this information, we can perform a relative trade on the skew of these Indices, even more if we know that this situation had happened several times in the past and on always these two values converged to the same value.

I invited you to create your own trading strategy based on this discrepancy. My strategy is coming soon.


[1] Percentiles are calculated using data from February 2008 – July 2012 

Monday, July 30, 2012

Binomial Options Calculator

With this spreadsheet you are going to calculate the price of an option using the binomial model. This calculator is flexible in tree dimensions, Put or Call, European or American and number of nods in the tree. Furthermore, you are going to be able to calculate Delta and Gamma of the option.



Wednesday, July 25, 2012


Looking Forward: What's next for Greece Equity Index?


The idea of this work is to compare the evolution of the European Equity Indices, with a focus on Greece, with the behavior experienced by the Indices of the Countries that had a Sovereign Default experience in the past. In particular, for this analysis we are going to use Russia, Indonesia and Argentina.

First of all, we are going to take a look at the evolution of the Greece Equity Index since its last peak occurred in January 2010 and compare it with the one performed by the other Indices in the past.

As we can see in the following graph, Greece Equity Index is now at a lower level than the bottom point of the Indonesian Equity Index after the default of its Debt in 1998 and at the same levels of Argentinean Index after its default in 2001, with a loss of more than 75 percent points (p.p.). However, the Russian Index decreased by 94 p.p. after the 1998 crisis, 14 p.p. less than the bottom level of Greece Index.


Equity Indices – Historical evolution

The immediate question is, what’s next for Greece? Is going to follow the Argentinean path, with a recovery in the Equity Index level in 22 weeks (almost half of the downside period), or would be the Russian path, with a deeper drop and a slow recovery along a five years period? On the other hand, Indonesia showed a fast recovery and then a double dip. Despite the way and the period, these three countries recovered together and almost at the same time after 2002, in part because of same changes in the global economy.

Equity Indices – Behavior after the bottom


Which one is the most likely scenario for Greece? What changed after 2002 that made these countries recover the pre-crisis levels in their Equity Indices? To determine this we are going to find the principal drivers that changed its trend after the 2002 and helped these countries to leave the crisis behind.

The first driver was the World GDP. As we can see in the next graph, between the beginning of the crisis in Russia and Indonesia and going through theirs and Argentinean Indices bottom points, the World GDP remained almost flat, with a cumulative growth of 6% between 1997 and 2001. On the other hand, the recovery of the three of these countries occurred between 2002 and 2004 in a scenario of 27% of World GDP growth.

World GDP at current prices


The future scenario for the World GDP looks more like the one of the end of the 20th century than the one of the beginning of the 21st century. If we take a look at the three biggest economies, we find that United States is facing a declining on its growth or at least troubles to recover the growing path, the Euro Area is coming from a slowdown in the last year that looks more like to becoming into a recession than into a recovery and finally the growth in China is definitely below the 10% last century mean.

So, as regards to this driver, the future of the Greece Index looks more like to be characterized for a couple of years of a slow recovery, maybe after a deeper drop, than for a fast one.

The second one, more than a driver was a common characteristic of these three countries, and it was a devaluation on their currency exchange rate of about 75%, with the corresponding improvement in their international competitiveness and the effect of the imports substitution. It is important to mention that the currency devaluation was a characteristic of the start and bottom period of the crisis than of the recovery.


Indices Evolution and Exchange currency rates


The devaluation of the exchange rate seems to be a necessary condition for the recovery of the Economy, or at least it was for most of the countries with debt problems in the past.

It is important to remark that devaluation would have a big impact on Greece GDP. One important part of Greece GDP is tourism. In 2001, before Greece had entered into the Eurozone below a common currency (EURO), the exports of travel services had represented almost 50% of the services exports and more than 30% of total exports, however at the end of 2011 these ratios were 33% and 21% respectively.

It is clear that with devaluation there is a good margin for that activity to increase, Mykonos is going to be cheaper than Barcelona for European tourists for example, been a good start for the Greece economy recovery in general. To put this in perspective, Argentinean exports/GDP ratio before devaluation was 11%, for Russia 25% and for Indonesia 26%. This ratio for Greece is around 24%.

However this Monetary Policy instrument is not available for Greece and the other members of the Euro Zone. Furthermore, the decision of devalued the currency for Greece includes an exit of the Euro Zone, which implies more difficult issues than just devaluation.

On the other hand, a devaluation most of the times come with a drop in the Equity Index, so if Greece is going to need a devaluation of its currency, or in this case an exit from the Euro Zone, the impact of this decision in the Index is going to be big, putting it into a lower level.

Just like the first one, the second driver direction point into a lower level scenario for Greece Index.

The third driver is the commodities prices, this variable is important because the exports of commodities in these countries represent more than 30% of the total exports. In particular for Russia the crude oil and the oil products represents more than 50%, for Argentina the primary products together with the energy ones sum around 35% and lastly for Indonesia the products related to the mining activity account 30%.

The following graph shows the evolution of the commodity prices indices and we can see how the agricultural and energy commodities showed an increase in its prices of 43% and 61% respectively between 2002-2004, while the ones related to the industrial minerals rose 28%, with the corresponding increase of 40% for Argentina and 80% for Russia and Indonesia in the exports of these products.

Commodity Price Indices Evolution


















For its part, Greece Oil exports represent 30% of total exports of goods and 13% of total exports, so in some sense we can expect an impact of this driver on Greece economy but maybe not as big as the one saw in the other countries.

Since the crisis in Greece started to present, the oil price was in an upward trend and trading in a range between 100 and 120 US dollars per barrel, closer to the peak price of 2008 than to the historical average prices. However there is a chance the oil price to go back to the historical maximum (QEIII), the scenario is completely the opposite of the previous crisis because commodities in general and oil in particular were in historical minimums.

Like the first two, the last driver doesn’t look like to be on the Greece side neither.

Conclusions

In this paper we follow the evolution of the Equity Indices of the biggest sovereign defaults in the contemporary history, Russia, Indonesia and Argentina, to evaluate the beginning, deepening and recovery of these countries.

To do it, we used three different drivers, the World GDP growth, the depreciation of the currency exchange rate and the commodities prices, to explain the recovery of the indices of these countries. Once we had the drivers, we use them to evaluate the Greece’s actual situation in order to forecast which one is the next step of the Greece Index. The projections of these drivers are not good news for Greece,

Firstly, the World GDP seems not likely to channel a growing trend of around 30% like it did in the beginning of the last century, instead is showing signs of weakness or even recession in some of the more important economies.

Secondly, at least for now, devaluation is not an isolated decision for Greece like it was for the other countries, it also means an exit from the European Union with uncertain consequences not only for Greece economy but also for the world in general, with a possible negative impact into the first driver, the World GDP.

Lastly, unlike the scenario faced by the other countries 10 years ago, the commodity prices are near the historical maximum levels and, unless they keep breaking maximums and combine with a scenario of a slowdown in the global economy, the more likely direction is down.

In conclusion, all the factors analyzed in this work, point that the Greece Equity Index is likely to be in the bottom zone than in the recovery one, with more chances of hit a lower level or face a slow recovery during a long period (Russian path) than follow the Argentinean path, with a fast recovery coming.

Tuesday, July 17, 2012

Attractive Cross-Asset Hedges for EZ Tail Risks

Here is one of the papers I published together with Ibrahim Gassambe at Roubini Global Economics.
The paper is focus on the best (Risk/Return/Premium Analysis) way to hedge a Euro Zone tail risk event using Cross-Asset put options.
Link to the paper

Wednesday, May 30, 2012

PDE SOLVER

Today I present a PDE solver applied to options valuation. The interesting thing of this model is that you not only get the price of the option but also  the price of it for all the possible Spot prices of the underlying.

Friday, May 4, 2012


Modeling Euro Area Sovereign Bonds
An application

In this project we show the interaction between quantitative and qualitative analysis to perform an strategy with Eura Area Sovereign Bonds.


First we built a quantitaive model to valuate risky bonds using the risk free rate and default probabilities as a parameters. Then we make an analysis about the past behaviour of certain parameters in order find some patterns to help us have a better understanding about the possible future scenarios for them. Finally, using the model we quantified the effect of changes in the parameters to know how would be the bond prices if our view actually occurs.




Looking back: An Analysis of the Evolution of the Europear Sovereign Bond Crisis



Today I present an analysis of the evolution of the CDS spreads for different countries of the Euro Area for 2010 and 2011. It is interesting to observed how this Crisis was changing over time from a "Peripheral Economies Crisis" (Greece, Portugal and Ireland) to a "Important Economies Crisis", like Spain and Italy (third and fourth nominal GDP contributors of the Area). Leaving an important question for the future, Is this crisis going to transform into a "Key Economies Crisis"?

The idea of this paper is to show the past behavior of the Credit Default Swaps (CDS) spreads for different countries of the Euro Area. The focus is on the years 2010 (especially the second and third quarter) and 2011 (third quarter), when the European Sovereign Bond crisis reached its worst levels.

To perform the analysis, we decided to pick seven countries in order to see the evolution of the CDS spread of each of them over time. These countries are Greece, Portugal, Ireland, Spain, Italy, France and Netherlands. Furthermore, we decided to classify them in four different categories,

During the first quarter of 2010, Portugal, Ireland, Spain and Italy used to live in the second category (between 100bp and 250bp). However, after a second quarter characterized by high volatility in the spreads of all these countries, during the third quarter the first two jumped into the third category and end up the year with a more pronounced positive slope than the second ones, showing the first differentiation between these countries’ spread.

On the other hand, Netherlands and France showed a more stable behavior with a small positive trend at the end of the year, especially France which finished the year in the second category. In this graph, we can see how the different countries start to differentiate of each other, with Portugal and Ireland lying in the third category, Spain and Italy in the second one and France and Netherland in the first one.

Selected European Countries - CDS Spread 2010
 (Basis Points)

If we move ahead to 2011, the next graph shows some interesting things. First of all, Portugal’s and Ireland’s CDS spreads jump to the fourth category, following the previous year Greece’s CDS spread trend. 

Secondly, the CDS spread levels of Spain and Italy lived in the third category most of the second half of the year, finishing it on that category. Thereby, they practically replicated the behavior of the previous year of Portugal and Ireland.

Lastly and maybe more important, the CDS spread of Netherlands and France, definitely broke the level of the first category (100bp) with a marked positive slope. Furthermore, France ended the year 2011 close to the upper bound of the second level, with a lot of similarities to Italy’s 2010 performance.

Selected European Countries - CDS Spread 2010/11
 (Basis Points)


It is interesting how the countries seem to move in pairs, replicating year after year the patterns of its neighborhood pair, for example Spain and Italy seem to replicate in 2011 the trajectory of Portugal and Ireland, and the same for France with Italy.

In summary, we followed the evolution of the CDS spread of most of the principal countries of the Euro Area. We showed that in the last 2 years the Sovereign Bond Crisis seemed to be transformed from a crisis in the peripheral economies (Greece, Portugal and Ireland) to important economies, like Spain and Italy (third and fourth nominal GDP contributors of the Area). Moreover, France, the second biggest economy of the Area, started to show at the end of 2011 the same pattern than Spain and Italy in 2010.

Some questions to think about them: 
  • What is the next state for the Europear Sovereign Bond Crisis? 
  • Are France and Netherland the future Italy and Spain? 
  • In this scenario, is Germany still a Risk Free Economy?
  • Are the receipts that didn’t work for developing countries, like reducing budget expenses, going to work for Europe? What is the plan b?

Ezequiel Zambaglione

(Special thanks to Sebastian Ummels who contribute a lot to the development of this work)

Monday, April 23, 2012

Interpolation

This is a file help you to perform linear, polynomial or cubic spline interpolation. Is a flexible file that let you choose the kind of interpolation and the amount of original data points. Usefull for interpolate Interest Rates, Implied Volatility, etc.

Options Calculator

Here I share with you an option calculator using Black-Scholes formula. With this calculator you are going to be able to obtain the Price and all the Greeks for European Calls and Put Options

Thursday, April 19, 2012

Informe Banco Central de la República Argentina

Deuda Externa del Sector Privado


Some of my work at the Central Bank....good memories

Principal Components Analysis on US Treasury yield curve

In this paper we analyse the evolution of the PC of the US Term Structure in the last ten years, and the effect of the FED interventions on them.

I wrote this paper with Andrés Jaime and Julio Ruiz. Special thanks for them. Code with MATLAB

Linear Regression Analysis

Here I applied Linear Regression Analysis to a hipotetical data set. This is a good guide to don't forget any step on the estimation and diagnostics necessaries to perform a good Linear Regression.
This time I use R for coding.

Tuesday, January 17, 2012

Trend following trading strategy for currecies

This is a strategy based on trend following where we use two moving averages to estimate the trend. The strategy was tested for EUR, CHF, SEK, and a portfolio with these currencies.

Here I worked with Ana Sokoleva, Andrés Jaime and Joaquín Tapia...ladies first of course

Tesis de Maestría en Finanzas

Tipo de cambio forward implícito y supuesto de ausencia de arbitraje en el mercado de bonos Argentino 

This is mi thesis of my Master in Finance, for now is in spanish (translation soon)

Résumé


This is my Résumé, you are welcome to take a look of it