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 Success story of a graduate
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It is difficult to foresee your future and estimate the long-term outcome of your decisions. Though it is rewarding to see that your efforts came though and thank people who helped you on your way. A few years ago, during the last year of my undergraduate studies in Economics at the Tallinn University of Technology, I learned about a new Master's degree in Financial and Actuarial Mathematics at the University of Tartu. In my undergraduate studies I had studied and become interested in a few seminal methodologies that proved to be successful in Economics and are deeply rooted in a set of mathematical and statistical methods, in particular, the Black-Scholes-Merton option pricing model and the Markowitz-Sharpe approach for optimal portfolio selection. After having explored the curriculum of the new Master's program at the University of Tartu, I felt very much exited about the opportunity that by attending this program I would be able to gain a deep understanding of various mathematical methods and their applications in Finance. I took this career path and applied to the program. My graduate studies at Tartu began in autumn 2000. In a first few weeks, while taking classes in probability, statistics, and numerical methods, I opened to myself a new world of Mathematics with its inherent abstraction and formalism. During my first semester, which turned out to be quite intensive, I learned one of the most important professional skills, in particular, the ability to concentrate deeply, understand difficult concepts relying on intuition, and formulate my reasoning in a concise mathematical way. In fall 2001 I took plenty of interesting classes. The one lead by Prof Raul Kangro was about using numerical methods to solve various problems for pricing of an option security, which is a financial security with the value and price derived from the asset prices underlying this option. I learned that under specific no-arbitrage conditions the value of the option satisfies a partial differential equation (PDE) and to obtain a value for the price of this option we need to solve this equation using appropriate numerical or analytical methods. It was an exiting class and every lecture I would discover a few practical problems and corresponding methods to solve them. I learned how to derive a PDE for option price under the famous Black-Scholes-Merton model and, importantly, how to solve this PDE using various finite-differencing schemes. I learned what Monte Carlo method is and how I can apply it to value options and to simulate option hedging strategies. Another rewarding class lead by Prof Kalev Pärna was about stochastic processes and their applications. I learned how to model the random phenomena using mathematical formulation and how this formulation can be used to study the predictability and unpredictability of the underlying objects. In particular, I was illuminated by discovering the connection between the stochastic calculus, PDE-s, option replication principles, and numerical methods. By the end of my first year in Tartu, I became hungry for a deeper understanding of the mathematics; I appreciated many subtleties of this field and knew that to comprehend the whole picture I would need to broaden my skill set. I decided to take an additional year for my graduate studies and take as many important undergraduate and graduate classes as I could. My decision was supported by my advisor Prof Kalev Pärna who advised me to pursue a second Master's degree in Mathematical Statistics. My second year in Tartu was one of the most interesting periods in my life -- busy lecture hours, numerous home-work assignments, and a rewarding feeling of accomplishment. What was important is the inspiration I felt from the faculty members of the Departments of Mathematics and Mathematical Statistics -- they all were available after-hours to discuss some problems, and they helped me understand the underlying concepts. Ultimately, after having attended two universities in Estonia and two in US, I must admit that my studies at the University of Tartu were the most valuable and fruitful experience. I finally graduated in 2003 with two Master's degrees: the one in Financial Mathematics and the second one in Mathematical Statistics. Then I began doctoral studies in Mathematical Statistics at the University of Tartu. In academic years 2004 and 2005 I attended two universities in US; first I spent an academic year at the department of Mathematics at Purdue University and then I spent another academic year at the Department of Industrial Engineering at Northwestern University. It also was a broad and beneficial experience. It was in June 2006, when I set foot on Wall Street by landing a summer internship at the investment bank Bear Stearns, then the fifth-largest US securities firm. That was an interesting time when for the first time I could apply my theoretical skills to solve practical problems arising in trading and risk-managing of financial derivative securities. It was rewarding to implement my own methods and see that they are useful for day-to-day operations. After a few weeks I was offered a full-time position, while still being officially a PhD student at the University of Tartu. At Bear Stearns, as a quantitative analyst (or simply "quant") I was working on different aspects of the volatility modeling. The volatility, with its many different interpretations, has extremely important consequences for options pricing and trading. On the one side, when talking about the asset historical volatility, we interpret the volatility as the uncertainty underlying the evolution of asset prices. On the other side, when talking about the option implied volatility, we interpret the volatility as a quantity we use while hedging an option. Option market participants are interested in having adequate modeling tools to describe the evolution of both implied and historical volatilities. In my job, every day I would realize how theory intercepts with practice. On the practical side, I would need to communicate with traders and senior officers and understand their needs and probable deficiencies of existing methods they were using. On the modeling side, I would propose a method how to improve the existing methodology or introduce a new one. On the implementation side, my proposed method would be implemented in the firm's trading system and made available to others. For example, to develop a stochastic volatility model, I would need a stochastic calculus to describe the random evolution of the asset price and its volatility and then assuming certain no-arbitrage condition derive the PDE for the option value. Then I would propose optimal analytical or numerical solution methods to solve the option pricing problem. Finally, I would write C++ code to implement this model and solution method in the firm's trading system, test my model and implementation, and provide an Excel spreadsheet with illustration of my methodology. In early 2007 I took a new job at Merrill Lynch, another Wall Street giant investment bank, as a quant in credit derivatives analytics group. Credit risk is a diverse notion, most often standing for the failure of a borrower to honor its payment obligations to a lender. Although the notion is itself very old, mathematical models to quantify and manage the credit risk are fairly young and, as is evident from the US subprime crisis, not very reliable. I have been working on various aspects of credit risk modeling starting from modeling a default event of an individual borrower up to modeling correlated defaults in a pool of borrowers. During my time at Merrill Lynch, it was instructive and challenging to see the turbulence in the credit market and observe how the market standard Gaussian Copula model, which has widely been used by market participants to quote and mark-to-market their credit positions, failed to reproduce observable market prices of traded credit instruments. It shows that a mathematical model can only provide a simplified description of the actual price dynamics and the model is as good as its underlying assumptions. When applying a mathematical model in practice, we need to test whether the model satisfies assumptions observed in practice and provides an adequate description of the underlying phenomena. If not, what is the optimal adjustment to be introduced without making the model too complicated? What happens if we change some of these assumptions? All this is a challenging modeling job, which a future quant or applied mathematician should start learning while being a student. I formally finished my graduate studies at the University of Tartu in summer 2007 by gaining a PhD in Mathematical Statistics. Looking back, I am delighted to have chosen the Faculty of Mathematics and Computer Science at the University of Tartu for my graduate studies. Here, I gained a strong background in mathematics and valuable skills of analytical thinking and problem solving, which are vital for my job. |