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.

Let's solve some equations!!

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.

Link to the paper

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

Spanish version published in Macrofinance Blog

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)