All the necessary definitions and concepts from the probability theory: random variables, normal and log-normal distributions, Brownian motion etc, will be explained in the course. Students will learn to use Bloomberg terminals with Excel these terminals are located in the Business School Library , will learn and do basic models in VBA and Matlab. Matlab is available through CUIT. Homeworks will be assigned on Mondays every 2 weeks, they are due on Mondays 2 weeks later. Homeworks will be distributed in class. Summary of lectures will also be distributed in class.

Homeworks may be challenging but they will contain many questions often asked at interviews and will teach helpful practical skills. There will be weekly recitation sessions by Helena Kauppila addressing and helping with homeworks. Time of these sessions will be announced later. These sessions are optional.

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Each student will be given a project. As a rare exception projects can be individual. Topic should be discussed with professor Smirnov appointment should be made preferably during office hours. After the group is formed its representatives e-mail project description proposal to professor Smirnov before October Students are welcome and encouraged to discuss project plans with professor Smirnov at office hours and Helena Kauppila at her office hours.

Some of the topics of past student projects will be given in class. These classes may be 30 minutes longer until 9. Attendance of these presentations is compulsory and attendance will be taken. Class Attendance. Students are highly encouraged to attend and not skip classes.

### Schedule, syllabus and examination date

So class materials and homeworks will be given in class and not through courseworks to encourage attendance. Grinold , R. Not required but highly recommended. Also not required but highly recommended. Readings will be assigned periodically. Additional finance articles will be distributed and assigned in class.

Midterm exam: Take-home midterm will be handed on September It is due on October We assume based on current information that final will be on December Final exam will have 2 parts.

The take-home part will be handed on November 14, it is due December In-class 1. Student project reports are due also December The final exam is compulsory and can not be rescheduled earlier or later. If there are conflicts with other exams please reschedule other exams. There may be occasional guest speakers.

## Financial Engineering, Financial Mathematics, and Quantitative Finance

They will be announced during the course. Course Requirements. Basic assets: cash, stocks, bonds, currencies, commodities. How they are traded. Forward contracts. Distribution of percentage returns and prices.

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Idealized assumptions of mathematical finance vs. Expectation, variance, standard deviation, skewness , kurtosis. Review of probability distributions and their properties. Normal random variables. Log-normal distribution and its properties. Distribution of the rate of return for stocks. Empirical evidence for the distribution of the rate of return for stocks and other assets.

A model of the behavior of stock prices. Mechanics of the futures markets. Margins, margin calls. Contango and backwardation, futures curves. As CDOs are very complicated securities, many investors bought them without fully understanding the mechanism how they work.

## Mathematical finance

In addition, the credits used in the packages were sometimes of questionable quality, the main issue that led to the current credit crisis. On the modelling side, determining the risk of a CDO investment requires an understanding of the correlation structure among the credits within it at least the correlation when it comes to defaults. Here, very simplistic models became popular in the industry and, on top of that, were regarded as perfect images of the real world. This proved to be wrong as soon as the first defaults occurred, and as a consequence the values of CDOs dropped dramatically.

Since credit derivatives and in particular CDOs had been enormously popular in recent years, the losses were huge and the consequence is the current financial crisis. Examples of more off-the-shelf applications of mathematics in economics include operations research methods applied to revenue management problems, queuing theory applied to storage problems, and dynamical systems used in macro-economic theory.

Although financial mathematics has been the most popular application of mathematics in economics in recent decades, this special theme contains reports on a variety of applications. The contributions can be grouped in three blocks, plus three survey-type papers:. While reading these contributions, one should keep in mind a key difference between this area of applied mathematics and more classical physics and engineering.

Questions relating to portfolio management Markowitz theory, efficient frontiers, CAPM are treated in detail in the fifth chapter. Chapters six and seven are dedicated to explain some basic characteristics of derivatives such as futures, forward contracts and options.

see Chapter eight deals with option pricing. A brief outline of the arguments that lead to the Black-Scholes formula is also included. Issues dealing with the use of derivatives in risk management are described in the ninth chapter: hedging, risk measures as value-at-risk VaR , speculating strategies with options, etc. These questions are treated by making use of a case study approach.

Finally, chapters ten and eleven are devoted to interest rates including term structure, the binomial model and a brief account of interest rates derivatives swaps, caps, floors. A textbook on financial mathematics like the one we are reviewing unavoidably faces a dilemma, namely the balance between mathematical rigor and financial concepts and their practical implementation. At the same time, despite its mathematically formal prose, the text is very readable. The relevant concepts are introduced gradually; often these concepts are preceded by numerical examples and in the end they are all given their corresponding formal definitions.

Almost all the main results are accompanied by corresponding proofs. A good deal of worked examples and remarks elucidate the associated financial concepts.