How can time series help in delimiting the relevant market.

Delimiting the relevant market is a key concept for the analysis of mergers and acquisitions. The theoretical framework introduced by the SNNIP test helps to understand the conditions needed to do it. Nevertheless, there exist so many methods and the scientific community does not coincide in what of them is better to use. In this article based on previous work[1], some methods grounded on time series are presented.

In general, the concept of relevant market is associated with arbitrage. In this sense, two regions belong to the same market when arbitrage is possible. Therefore, it is possible to check whether the prices of these areas hold a pattern of convergence. As exposed mainly in Haldrup (2003)[2] , we can differentiate two types of convergence:

Absolute convergence: it appears when there is perfect arbitrage with no transportation costs, then the stationary price difference between regions is zero. It can be expressed as:

limitRelative convergence: it is analogous to the previous concept but, in this case, transportation cost does not completely disappear. It can be expressed as:

limitTherefore, absolute convergence is a specific case of relative convergence for the case of α=0, which is mainly that transportation costs are equal to zero.

There are several methods used to analyse time series of prices. They are useful to define the relevant market. There are two main dimensions: defining the market of substitute goods and delimiting the area where a company is competing.

CORRELATION

Correlation is one of the most common methods used to analyse prices. In this sense, Stigler & Sherwin (1985)[3] proposed to do it with series transformed in logarithms to avoid problems arising from divergences in variance.

Ideally, two prices of goods or regions inside the same market should have high correlation in both logarithms and its first derivative (that works as an approximation of the growth rate).

This method presents many problems. Firstly, high correlations can be produced because of a spurious relation (Granger & Newbold, 1975)[4]. Moreover, Bishop & Walker (1996)[5] argue that highly volatile exchange rates can distort the results. Nevertheless, Haldrup (2003)[2] argue the since 90s exchange rates have a stable structure and, therefore, the analysis is not injured.

COINTEGRATION

Cointegration can be determined by the procedure defined by Engle & Granger (1987)[6]. In a more general insight, if time series are integrated of order 1, it is possible to use the Johansen’s test (1991)[7]. In this sense, Alexander & Wyeth (1994)[8] argue that a common market can be defined with only one cointegration relationship. In contrast, Haldrup (2003)[2] argues that the single market is determined with k-1, the maximum, cointegration relationships. Cointegration cannot be applied when one of the series is not integrated, that is, it is stationary.

Given that cointegration relationships can be understood as a log-run equilibrium, it is possible to define best response functions to find results corresponding to price-based models, as Bertrand’s Oligopoly.

FORNI’S TEST

Since cointegration procedure is based on unit roots tests, Forni (2004)[9] defined a way of determining the long-run equilibrium in a more flexible way. This test tries to analyse the stationarity of the logarithm of the ratios of both price series. It is possible to run different unit root test.

  NULL HYPOTHESIS
ADF They do not belong to the same market  (non-stationarity)
ADF-GLS They do not belong to the same market  (non-stationarity)
KPSS Both goods or regions belong to the same market (stationarity)

Figure 1 shows the time-series of the logarithm of the ratio of the price of two different goods. It is an example of relative convergence. Even with some outliers it is possible to see how the ratio fluctuates around an equilibrium. In this case, the test allows to conclude that the series is stationary. We could conclude that with the evidence extracted from this procedure, both goods are part of the same relevant market.

Figure 1: Ratio of two prices seeming to be in the same marketestacionario Source: Own elaboration in previous work [1]

Figure 2 shows the same time-series but for different goods. It shows an unclear pattern of co-movement between prices. Not only prices seem not be related but also, they seem to move away. In this case, the series is not stationary and thus, according with this test, we could conclude that both goods do not belong to the same market.

Figure 2: Ratio of two prices seeming not to be in the same market.
no-est   Source: Own elaboration in previous work[1]

From my point of view, for this purpose, unit root tests can be applied either with or without trend and intercept in the auxiliary regression. Initially, to test whether two goods or regions belong to the same market the trend is not relevant, since they should have a constant long-run equilibrium. In the case that the series were not stationary, repeating the test with trend would be interesting. It could explain if there exists a pattern of divergence between goods or regions. The intercept can be understood as the α coefficient exposed above. If it were zero and the test concluded stationarity, it could be a case of absolute convergence.

GRANGER CAUSALITY

Granger causality is based on the analysis of VAR models. In an easy approach, with VAR models we try to estimate the price of one good or area in function of the lags of the other price and its own lags. Granger causality analyses the null of all coefficient of the other price are zero. If the null is rejected, one price causes the other and they seem to belong to the same market.

It is possible to carry out the regressions in both ways, the first one for estimating a price and the second one for estimating the other. There could be causality in both ways but it is not a necessary requirement to conclude that there exists a causality relationship between them.

Prices displayed as the ratio of Figure 1, showed a two-way causality relationship. However, prices of Figure 2 did not show any causality relationship.

CONCLUSIONS

There are many methods to analyse if some regions or goods belong to the same relevant market. Apart from the ones exposed above, other price-based ways can be used as VEC models or PCA, and other non-price-based methods as the shock analysis or the Elzinga & Hogarty Test (1973)[10].

In general, different procedures do not use to issue contradictory answers, but they are not self-explanatory by themselves. They need to be complemented with each other to bring back the most accurate conclusion.

REFERENCES

[1] See García García, Alberto (2016). El mercado relevante: técnicas económicas y econométricas para la delimitación. Trabajo Fin de Grado. Universidad de Oviedo.

[2] Haldrup, N. (2003). “Empirical Analysis of Price Data in the Delineation of the Relevant Geographical Market in Competition Analysis. University of Aarhus, Economic Working Paper .

[3] Stigler, G. J., & Sherwin, R. A. (1985). The Extent of the Market. Journal of Law and Economics, Vol. 28, No. 3, 555-585.

[4] Granger, C. W., & Newbold, P. (1974). Spurious Regressions in Econometrics. Journal of Econometrics, 2;, 111-20.

[5] Bishop, S., & Walker, M. (1996). “Price correlation analysis: still a useful tool for relevant market definition. Lexecon.

[6] Engle, R. F. & Granger, C.W. (1987). Co-Integration and Error Correction: Representation, Estimation and Testing. Econometrica, 55(2), 251-76.

[7] Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 231-254.

[8] Alexander, Carol and Wyeth, John (1994) Cointegration and market integration: an application to the Indonesian rice market. The Journal of Development Studies, 30 (2). pp. 303-334. ISSN 0022-0388

[9] Forni, M. (2004). Using Stationarity Test in Antitrust Market Definition. American Law and Economic Review, 441-64.

[10] Elzinga, K. G., & Hogarty, T. F. (1973). The Problem of Geographic Market Definition in Antimerger Suits. Antitrust Bulletin, 18(1), pp.45-81.

Brexit: BGSE Community Analysis

We want to know what the BGSE community is thinking and reading about the Brexit.

brexit-624x437

We invite all Barcelona GSE students and alumni to share their early reflections on the potential economic consequences of the UK’s recent vote to leave the EU. Did you focus on a related topic in your master project? Are you working at a think tank, central bank, or consulting firm where your projects will be impacted by this decision? Have you seen any articles or links that you found useful for understanding what lies ahead?

Here are a couple of pieces we’ve found to get the discussion going:

After Brexit: What next for the EMU, EU and UK?
(ADEMU webinar)

The BGSE participates in A Dynamic Economic and Monetary Union (ADEMU), a project of the EU Horizon 2020 Program. Last week, ADEMU researchers held a webinar to discuss the Brexit.

Background:

Europe has grown out of its crises when reason and solidarity have prevailed, but it has also been devastated by its crises when fear and nationalism have taken the lead. Brexit, in the aftermath of the euro crisis, brings this dichotomy back to the foreground. Since 2010 there have been important advances in the development of the Economic and Monetary Union (EMU) and flexible forms of participation have allowed other EU countries, reluctant to join the euro, to share the basic principles that define the EU and have a common presence in the interdependent global world.

According to the panelists, Brexit raises 3 crucial questions:

  1. Should the EMU be accelerated to become a centre of gravity within the EU, or slowed down to avoid a centrifugal diaspora? If accelerated, how?
  2. Should an ‘exit’ country be allowed free entry to the single market and other EU public goods without accepting freedom of movement?
  3. Should the EU remain as it is, or increase its capacity to offer common public services (Banking Union, border security, research funding, environment, etc.), or limit its scope of activity to the EU single and integrated market?

Webinar Panel:
– Joaquín Almunia (Former Vice-President of the European Commission, honorary president of the Barcelona GSE)
– Ramon Marimon (European University Institute and UPF – Barcelona GSE; ADEMU)
– Gorgio Monti (European University Institute; ADEMU)
– Morten Ravn (University College London; ADEMU)

Moderator:
Annika Zorn (European University Institute; Florence School of Banking & Finance)


From Brexit to the Future
(Joseph Stiglitz)

Nobel Laureate and Barcelona GSE Scientific Council member Joseph Stiglitz shares some reflections in the wake of the Brexit decision


What are you thoughts on Brexit?

We want to know what the BGSE community is thinking and reading about the Brexit. Please share your ideas, favorite sources for analysis, or observations from economists you respect in the comments below.

Cross ownership and firm performance

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects by students in the Class of 2015. The project is a required component of every master program.


Authors:
Octavi Castells Pera, Jaime López Sastre, and Berenice Ramirez

Master’s Program:
Finance

Paper Abstract:

This paper assesses the impact of cross ownership on firm performance and industry competition through an analysis of shareholder’s networks in Spain using a panel regression model on a sample of non-financial listed companies between the years 2004 and 2012. The results show that there is a positive and significant effect of the number of connections a firm has with other industry rivals through the common ownership mechanism on its markup.

Read the paper or view presentation slides:

What can the risk neutral moments tell us about future returns?

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects by students in the Class of 2015. The project is a required component of every master program.


Authors:
Juan Imbet, Nuria Mata

Master’s Program:
Finance

Paper Abstract:

We test if the first four moments of the risk neutral distribution implicit in options’ prices predict market returns. We estimate the risk
neutral distribution of the S&P 500 over different frequencies using a non parametric polynomial fitting, and test if the first four moments of the distribution predict returns of the S&P 500. Our results suggest that there is no evidence on this predictability power.

Presentation Slides:

Photo Diary: Exams Winter 2015

How masters and PhD students are surviving finals this month…

Staking out a cozy corner in the library

 

It’s all about the snacks

 

Moments of Zen

 

A little help from our friends

 

Have a photo you’d like to share? Email it to thevoice@barcelonagse.eu or mention @barcelonagse on Twitter or Instagram

Greek Banks in the Headlines (Link Roundup) | Daily Updates

Evolution of news about Greek banks. Curated by @BankingUnion_eu (current student in the Master in Economics).

5 FEB

ECB collateral damages on Greece (Bruegel)

Greek banks will not have any liquidity problems, JP Morgan report‏ (Intelligent News)

Q&A: The ECB’s warning shot to Greece (Financial Times)

ECB turns off the taps, but Greek banks can still get funding (Open Europe)

Levine on Wall Street: Bearer Bonds and Greek Banks (BloombergView)

Greek banks hit after ECB snub, Athens rejects ‘blackmail’ (Reuters)

What are the implications of the ECB’s decision for Greek banks? (Macropolis)

Emergency Liquidity Assistance for Greek Banks: Explainer (BloombergBusiness)

What the ECB’s Move on Greek Government Debt Is Really All About (BloombergBusiness)

What you need to know about ECB’s Greek collateral decision (MarketWatch)

Eligibility of Greek bonds used as collateral in Eurosystem monetary policy operations (ECB Press Release)

4 FEB

European Central Bank resists latest Greek bailout plan (FT)

ECB set to back further liquidity assistance for Greek banks -paper (Reuters)

Greeks Spooked by Debt Clashes Put Cash Under Bathroom Tiles (Bloomberg)

ECB Readies Lifeline for Greek Banks (Handelsblatt)

The state of play with Greek banks’ liquidity (Macropolis)

3 FEB

Exclusive – Three Greek banks tap two billion euros in emergency funding: sources (Reuters)

Greek banks lifted by Syriza debt plan (FT)

First Germany, Now ECB Rejects “Latest Greek Bailout Plan” (Zero Hedge)

1 FEB

So Whose Problem Is Greek Debt, Anyway? (Forbes)

Greece Asks ECB to Keep Banks Afloat, Tsipras Pitches Deal (Bloomberg)

For Greece, Bank Trouble Looms Again as New Government Takes Shape (The New York Times)

What’s Going On with Greece and the ECB? (Medium)

31 JAN

ECB’s Liikanen – No lending to Greek banks if no deal by end of February (Reuters)

Greek Banks May Lose ECB Credit, Says Policy Maker Liikanen (The Wall Street Journal)

30 JAN

Greek bank debt plummets as investors head for the exit (Reuters)

Six things you need to know about Greek banks (CapX)

Europe’s Greek Test (The New York Times)

Greece Sets Up Cash Crunch for March Telling EU Financial Bailout Is Over (Bloomberg)

How Greece Can Run Out of Cash and What ECB’s Draghi Can Do (Bloomberg)

S&P warns on Greek banks (FT)

Greece’s New Government Is About To Start Debt Negotiations With Its Eurozone Partners (Business Insider)

29 JAN

Greek Markets Buckle. New Coalition Government Fans Investors’ Fears of Eurozone Exit (The Wall Street Journal)

Greek Bank Shares Edge Back Up Off Record Lows (The New York Times)

Greek banks find support after fall (FT)

Greek bank crisis leaves time short to strike debt deal (FT)

Greek Markets Steady as Banks Rebound (The Wall Street Journal)

Greek Banks Are Ticking Time Bombs (Bloomberg)

Greek bank deposits fall as pre-election tensions rise (Reuters)

Greek Bank Deposit Flight Said to Accelerate to Record (Bloomberg)

Greek Banks at Mercy of the Fates (The Wall Street Journal)

Greek Bonds Halt Slide as Banks Rally; Ireland Borrows for Free (Bloomberg)

Greek banks rebound amid debt talk hopes (The Telegraph)

28 JAN

Greek banks lose €8bn in three days since Syriza victory as liquidity crisis feared (The Telegraph)

Greek Stocks Crash, Bonds Plummet, Banks Have Worst Day Ever (Zero Hedge)

Thinking About the New Greek Crisis (The New York Times)

Greek Banks Have Just Lost A Third Of Their Value — Here’s Why (Forbes)

Greek banks are getting shattered (Business Insider)

Greek banks extend slide to peg back European shares (Reuters)

Greek bank stocks hit record lows after leftist poll win (Reuters)

Greek banks plunge as new government challenges bailout (CNN)

Now We ‘Know’ Greek Banks Are Really In Trouble (Zero Hedge)

ECB Supervisor Nouy Says Greek Banks Strong Enough to Survive (Bloomberg)

Renewed plunge in Greek banks hits European shares (Reuters)

Greek bank stocks and deposits hit by default fears (CNBC)

$11 Billion Wiped From Greek Banks on Nationalization Threat (Bloomberg)

The Death of Fixed Income

alumni


Alex Hansson
’13 (International Trade, Finance and Development) is an Analyst at Tribus Capital Partners in Zurich, Switzerland. Previously he was External Asset Management Analyst at Credit Suisse.


 

cartoon
Source: The New Yorker

A few weeks ago I found myself sitting in the James Joyce Wine Cellar in Zurich listening to a talk by the Chief Investment Officer of one of the world’s largest asset managers’ fixed income division. Surrounded by ageing wine bottles and Swiss bankers in grey suits, the CIO put down his glass of Chateau Neuf du Pape and proclaimed, “You know, I’ve been investing in fixed income all my career, but I feel obliged to tell you that fixed income as an asset class is dead.” That was the last sentence of the speech.

Now I don’t frequent too many of these events, but ending a presentation on that kind of a bombshell was not something that I’d ever experienced before. The Swiss bankers around me shifted nervously in their seats thinking something else was coming. But the CIO did not follow up the statement with any caveats. He was undoubtedly out to provoke and had we pushed him a little he would have most likely followed up his statement with the usual spiel that one should be careful with statements like ‘this time it is different.’ He would have probably added that fixed income in terms of developed markets sovereign and corporate bonds would at some point in the future again be an interesting investment.

Nonetheless, finding out fixed income was dead was pretty exciting. Moreover, the statement was in line with a trend I had been witnessing for the past couple months whereby capital was flowing into a new asset class – alternative fixed income.

But, before moving on to this, it is worth spending a few minutes on the death of fixed income, whether temporary or not. Classic portfolio management theory will tell you to put 60% of your assets in equities (e.g. at its most basic through a S&P 500 Index ETF) and 40% in bonds (e.g. at its most basic through a Bond Index) in order to achieve diversification and lower the portfolio’s volatility. Without getting too deep into the technicalities, the thinking goes that equities outperform bonds in the long run – hence the overweight. However, bonds are included because they lower the volatility and increase the diversification of the overall portfolio. They lower the volatility because they are less risky than equities. Moreover, bonds have historically moved inversely to equities and this diversification effect has served the purpose of smoothing out the return profile of a balanced portfolio in times of market turbulence. Seeing as, nearly all investors have regular liquidity needs for, for instance, a regular mortgage payment, a smoother albeit lower return profile in the long run is more attractive than high volatility with a higher return in the very long run.

So what has changed? Norman Villamin (CIO Coutts) was recently quoted as saying that bonds used to offer an asymmetric payoff relative to equities whereas now you are left with a “symmetric asset class.” Put another way, bonds still serve the purpose of protecting capital when equities are down but no longer give you any meaningful upside. In other words by having 40% bonds you lower volatility but you no longer achieve diversification. Explaining exactly why, at least from a developed markets perspective, is not straightforward. Some analysts have highlighted that rates have been kept low to encourage lending given the slower than expected recovery in the US and Europe. Other analysts have pointed to lower inflation and central banks not feeling the pressure to increase rates. In any case, with very low returns you also have very low volatility. With low volatility even if this effect moves inversely to equities it will not be ‘strong enough’ to provide the desired counterbalancing effect. Think of two grown men on a seesaw where one gets replaced by a child, no matter how much the child jumps up and down on the plank, they will not significantly propel the man into the air. Whatever the reasons for this phenomenon, most seem to agree that a low rate environment will be the norm for some time to come.

Many investors realize that if rates remain low it will become more difficult to find bonds yielding attractive returns without taking on excessive risk. In terms of fixed income this generally means looking towards emerging market debt or distressed corporate bonds. To be clear some investors have successfully gone down this route, such as, Michael Hasenstab (CIO Franklin Templeton) who has became famous for his bullish speeches on Ukrainian debt. Nonetheless this dynamic has led to many investors leaving fixed income in favor of equities. That trend is clearly reflected by the fact that the largest fund by assets under management has over the last year shifted from the PIMCO Total Return fund (a fixed income product) to the Vanguard Total Stock Market Index (an equity product). The leaving of Mr. Gross from PIMCO no doubt also contributed to this shift.

With the recent prolonged bull market most investors have shut their eyes to the increased volatility and enjoyed the attractive returns they have seen from their portfolios. However, some sophisticated investors have elected not to move their fixed income exposure to equities. Some have chosen to put assets into well-known alternatives like private equity or real estate. But these asset classes do not offer the same advantages that fixed income did.

As outlined above fixed income was liked because, first, it was relatively low risk. Second, it paid a steady regular coupon, which was liked not just by private investors but especially pension and insurance funds, which have regular liquidity needs. Third, it paid a handsome return of anywhere from 5.00% to 8.00% (historically seen). To put that into perspective, a ten year German Government Bond pays you less than 1.00% currently. A private equity or real estate investment conversely can mean having to lock up capital for ten years, with no regular coupon payment, and with no guarantee for handsome reward.

Given this, many of these sophisticated investors have turned to a different asset class that has emerged largely as a product of new lending opportunities. It is often referred to as Alternative Fixed Income. These opportunities have to a large extent emerged as a product of new banking regulations. Simply put, banks have been forced to move away from certain types of lending and new non-bank credit providers have stepped in to fill this void offering new investment opportunities. Indeed, according to Alliance Bernstein, since 1980 the nonfinancial corporate and mortgage credit outstanding has grown by ca. USD 18.9tn whereof USD 15.0tn can be attributed to non-banks.

This trend of lending by non-banks has been accelerated largely as a product of post-crisis regulation. In Europe, the most important regulation framework for this trend has been Basel III. This framework stipulated that banks now have much higher capital requirements as well as having to take on higher operational costs for certain types of lending. This has been most pronounced for investments with longer investments horizons, which therefore cannot match bank-liability structures subject to daily liquidity requirements.

There are literally hundreds of structures that have emerged to take advantage of this systemic shift. The biggest opportunities for alternative credit providers have been in corporate loans, commercial real estate loans, residential real estate loans, and infrastructure loans. Many new organizations have been set up and are raising capital from investors in order to lend to corporations and real estate developers in the same way banks used to. The lenders pay a coupon on the loan, the new firms take a cut, and the investor gets a regular coupon payment at a tolerable risk and a much higher return than they would have in traditional fixed income.

This systemic shift has created opportunities along the entire supply chain of lending. It stretches from the most logical to the most niche areas you can think of, and no doubt this is just the beginning. Below I will give two examples of the most common constellations.

Most commonly you see new organizations made up of former bankers. They leave or are made redundant by their employer. They take with them an intimate knowledge of that bank’s loan book as well as the skillset to analyze other banks’ loan books. They then raise capital in a fund structure (funded by our sophisticated investors above) and begin buying loans from banks that can no longer be kept on their balance sheets. This can take many different forms. The easiest is a pure purchase at a discount where the new organization takes over the loan. Typically this happens via a Collateralized Loan Obligation (CLO) which is a securitized asset backed by a pool of debt. Another variety is a situation where banks have debt on their balance sheet which is highly attractive from a return perspective but which they cannot keep on their balance sheet. They therefore use something called Regulatory Capital Relief Trades (CRTs) in order to temporarily transfer risky assets off their balance sheets to one of these new organizations which in turn charge interest on the assets while on their balance sheets. Finally you have situations where the bank will give an organization access to their pipeline of loan opportunities. This setup is rarer and requires a very close relationship between the bank and the new organization. Essentially, these new organization can sift through bank’s pipeline of lending opportunities and chose to take on any loans they find attractive. In return the bank receives a share of the profits.

The other more common constellation of new organizations is direct loans that banks used to be able to do. Indeed, many of these organizations are whole teams that used to do the same thing at their former employers. A great example is Renshaw Bay. Renshaw Bay was setup by the former co-CEO of J.P. Morgan’s Investment Bank – Bill Winters. The firm runs a real estate strategy that is “focused on direct, whole loan origination of commercial real estate loans… and seeks to take advantage of the lack of financing available to real estate borrowers”. They also run a structural finance strategy, which looks to “capitalize on opportunities driven by regulatory change and the retreat of capital.” There are now new organizations (or old organizations which have seen a significant uptick in demand) that are doing the same thing in corporate loans, real estate loans, infrastructure loans, or even leverage loans to private equity firms.

It is still relatively early days and no one yet completely understands the full implications of this systemic shift. Perhaps the setup is better, seeing as you have more specialized niche players, often with much of their internal capital at risk, and unhindered by bureaucracy associated with banks running these new organizations. Or perhaps this setup is riskier, since at the same time you also have small, inexperienced, and at times highly leveraged organizations with less oversight then banks used to have. Added to this increasing numbers of pension funds and insurance companies are investing in these structures. Undoubtedly there will be some financial cowboys who have cut corners in order to have first mover advantage. At the same time you will undoubtedly have a lot of smart people who will make themselves and their investors a lot of money. Clearly, it is going to be very interesting to monitor these developments to see whether this shift turns out to be a good one or a bad one.

Too-many-to-fail: a theoretical approach

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects by students in the Class of 2014. The project is a required component of every master program.


Too-many-to-fail: a theoretical approach

Author:

Jaume Martí

Master Program:

Finance

Paper Abstract:

The recent financial crisis has generated enormous economic and human costs. New regulatory framework has been proposed in order to provide banks with better incentives.

My goal in this project is to theoretically explain several market failures that happened prior to the financial crisis and propose a model that captures these phenomena in the banking sector. To end up, I suggest different macroprudential measures that could be undertaken with the ultimate objective of providing a more stable financial system.

Realized Volatility Estimation – Barcelona GSE Master Projects 2014

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects by students in the Class of 2014. The project is a required component of every master program.


Realized Volatility Estimation

Authors:

Miquel Masoliver, Guillem Roig, Shikhar Singla

Master Program:

Finance

Paper Abstract:

The main purpose of this study is to try to find the optimal volatility estimator in a non-parametric framework. In particular, this study focuses on the estimation of the daily integrated variance-covariance matrix of stock returns using simulated and high-frequency data in the presence of market microstructure noise, jumps, and non-synchronous trading. This work is structured in three building blocks: (i) price processes are simulated in the presence of jumps and market microstructure noise. This allows us to obtain some insight about the estimators’ performance. (ii) The aforementioned realized volatility estimators are applied to high-frequency data of the S&P 100 stocks of October 27th 2010 using 5-second, 10-second, 30-second, 1-minute and 2-minute time intervals. (iii) We use the estimated covariance matrices to construct the global minimum variance portfolio for each sampling frequency. These global minimum variance portfolios are used to build 30 day ex-post portfolio’s returns and we use the variance of these returns to compare between the performance of the estimators.

Read the full paper or view slides below:

Interest rates after the credit crunch crisis: single versus multiple curve approach

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects by students in the Class of 2014. The project is a required component of every master program.


Interest rates after the credit crunch crisis: single versus multiple curve approach

Authors:

Oleksandr Dmytriiev, Yining Geng, and Cem Sinan Ozturk

Master Program:

Finance

Paper Abstract:

For interest rate derivative pricing, 2007 crisis was a turning point. Prior to the crisis, market interest rates showed consistencies that allowed the use of a single curve for both forwarding and discounting. After the crisis, the inconsistencies in the market interest rates led to development of a new method of the pricing interest rate derivatives, which is called Multi-Curve Framework. We studied the influence of the multi-curve approach on the interest rate derivative pricing. We calculated and compared the price of a simple swap in both multi-curve and single curve approaches. We suggested the generalization of the lattice approach, which is usually used to approximate the short interest rate models, for milti-curve framework. This is a novel result, which have not been developed in the scientific literature. As an example, we showed how to use the Black-Derman-Toy interest rate model on binomial lattice in multi-curve framework and calculated the price of the 2-8 period swaption in a single (LIBOR) curve and two-curve (OIS+LIBOR) approaches. This technique can be used for pricing any interest rate instrument.

Read the full paper or view slides below: