Quantitative Finance

2019/2020

Учебный год

ENG

Обучение ведется на английском языке

10

Кредиты

Кто читает:

Международный институт экономики и финансов

Статус:

Курс по выбору

Когда читается:

4-й курс, 1-4 модуль

Course Syllabus

Abstract

The course provides coverage of important topics in modern Quantitative Finance and Risk Management at the advanced undergraduate level. Itis intended for the 4th-year undergraduate students of the International College of Economics and Finance, High School of Economics, Moscow. Particular attention is given to the topics such as the Efficient Market Hypothesis, financial markets microstructure and types of arbitrage, general principles of modelling the price dynamics of financial assets, market risk and other types of financial risks, Value-at-Risk (VaR) approach and applications, modelling of extreme market events, VaR analysis for financial derivatives using the Kolmogorov equations framework, modelling of periodic and quasiperiodic trends in time series in connection with technical analysis, and the foundations of high frequency arbitrage trading. The topics covered in this course will enable the students to develop the theoretical knowledge and practical skills required for successful working with multiple types of risks in modern financial markets, both Russian and international. The course is taught in English. Prerequisites for the course areElements of Econometrics and Microeconomics. Good command of methods of calculus, general probability theory and mathematical statistics are also required for the course.

Learning Objectives

• to give students insights in the functioning of financial markets, understanding of measuring and forecasting financial risks
• to give students instruments required in order to analyze issues in asset pricing and marketfinance
• to familiarize students with recent empirical findings based on financial econometric models
• to ensure students have a good command of basic econometric techniques and understand practical issues in the forecasting of key financial market variables

Expected Learning Outcomes

• - Distinguish time series from other data forms
• - Be able to find time series moments, autocorrelation functions and other characteristics
• - Be able to show that the time series is white noise
• - Distinguish different forms of ARMA models
• - Be able to use the concept of stationarity and make connection to different ARMA representations
• - Be able to prove that time series is weakly stationary using definition and different criteria
• - Be able to represent stationary AR model as MA with infinitely many parameters
• - Be able to estimate ARMA models using software
• - Be able to use the concept of volatility
• - Be able to use (G)ARCH models are and their basic properties
• - Be able to estimate (G)ARCH models
• - Be able to use the concept of cointegration and Granger Causality
• - Be able to show that VAR model is weakly stationary
• - Be able to show that one variable Granger causes another
• - Be able to use and apply stylized facts of financial data and asset returns, in particular
• - Use extensions of basic ARCH/GARCH models and connect them to the financial data stylized facts
• - Be able to determine if the forecast is optimal
• - Be able to compare the quality of two and more forecasts of the same variable
• - Be able to relate he concept of efficient markets to the ARMA-GARCH models
• - Be able to register basic data scooping mistakes the researcher might do when he tries to show the significance of particular variables in his econometric model
• - Be able to calculate VaR and Expected Shortfall (ES) using different (parametric, non-parametric and semiparametric) methods
• - Be able to compare VaR and ES forecasts
• - Be able to show that constructed VaR and ES forecasts are optimal
• - Be able to use the concept of diurnality
• - Be able to construct and estimate empirical models for intraday data

Course Contents

• Basic time series concepts
  Many problems in quantitative finance involve the study of financial data. Such data most often comes in the form of ‘time series’, which is a sequence of random variables that are ordered through time. Before moving on to financial applications, we must first cover some fundamentaltopics in time series analysis, such as autocorrelation, white noise processes and ARMA processes. This topic is the most theoretical one in the course, and it may not appear too related to finance, but it lays the foundations for the (more interesting) topics we will cover later
• Testing for stationarity
  Testing for stationarity: graphical techniques and the formal unit root tests. (Augmented) DickeyFuller tests. Other tests of nonstationarity.
• Modeling asset return volatility: introduction
  Risk plays a central role in financial decision making, and it is thus no surprise that a great deal of effort has been devoted to the study of the volatility of asset returns. This effort has paid large dividends: volatility modeling and forecasting methods have been shown to be very useful in many economic applications. In this topic we will cover some of the most widely-used models for modeling volatility,discuss the estimationofthesemodels, andmethodsoftestingfor volatilitypredictability.
• Vector Autoregression
  Dynamic interdependencies of financial variables can be uncovered using VAR analysis. Impulseresponse function. Granger causality
• Empirical features of financial data
  Introducingsomeconceptsofdefining anddescribing financialdata,wealsodiscussmainstylizedfacts of returns.
• Modeling asset return volatility: extensions
  In this chapter we discuss extensions of the basic ARCH/GARCH class of models, both univariate and multivariate. Univariate extensions havebeen proposed to capture moredetailed features of asset return volatility, such as the so-called “leverage effect”. Multivariate extensions of the GARCH model are used to assist with financial decisions that involve more than one risky asset, such as portfolio decisions or risk management.
• Evaluating forecasts of risks and returns
  There are often many competing statistical models available for use in the forecasting of a particular financial variable. There are also many commercially available forecasts, issued by brokers or mutual funds. How do we determine whether the forecast is good or not? How do we determine which model or forecaster is best? These two questions relate to forecast evaluation and comparison. A third question that arises is whether we can take a collection of forecasts and combine them somehow to get an even better forecast. We will cover methods for answering these questions in this topic.
• The efficient market hypothesis and market predictability
  Much of modern quantitative finance relates to methods and models for predicting aspects of asset returns, and yet the classical theory of efficient markets may appear to suggest that asset returns should be completely unpredictable. In this topic we relate the concept of efficient markets, defined in various ways, to the evidence of predictability of financial variables and reconcile the empirical evidence for asset return predictability with the concept of an efficient market.
• Risk management and Value-at-Risk: models
  Measuring and managing the exposure to risk generated by a trading desk, a structured product, or a traditional portfolio is one of the most important and interesting parts of quantitative finance. Modern risk management focuses heavily on a measure of risk known as “Value-at- Risk”, or VaR. This is partly due to some advantages of this measure over variance, and partly due to regulation (the Basel Accords are based on VaR as a measure of risk). In this topic we will introduce VaR formally and discuss some of the most common models for measuring VaR.
• Risk management and Value-at-Risk: backtesting
  An important part of managing risk is testing how well your risk models are performing, a task known in the risk management literature as backtesting. Such tests can also be useful for indicating ways to improve risk models. This topic will cover some methods for backtesting VaR models.
• Modeling high frequency financial data
  Traditionally, empirical studies in finance employed data at the daily and monthly frequencies. Many models and methods have been developed for the study of such data. Recently, high frequency (intraday) has become available to researchers, and empirical market microstructure is now an established sub-field within finance. Many of the methods developed for lower frequency data are applicable to high frequency data, butthere are a few places where differences exist, and wewill study two ofthese in this topic. How one treats the massive amounts of high frequency data available should depend on the problemthe researcherwishes to address. Inmany cases,thequestioncanbe addressedbyaggregating the ‘tick’ data up to a certain frequency and then analyze the sequence of aggregated returns. Doing so makes the data evenly spaced, and thus more similar to well-studied low frequency data. Many questions, however, are best addressed using tick data, meaning that we mustfind ways of dealing with the irregularly-spaced observations. Another problem that arises in certainanalyses of high frequency data is seasonality. Seasonality is a well-studied problem in macro- and micro-econometrics, but is not generally a concern for financial econometricians. Intra-daily patterns (called ‘diurnality’ rather than ‘seasonality’) in certain measures are significant and must be dealt with. Three places where diurnality in high frequency returns has been found to be prominent are in the conditional variance, in bid-ask spreads and in trade durations.

Assessment Elements

• December exam
• Midterm test
• home assignments
• Final exam
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• UoL exam
  UoL exm is not included in overall grade for 4th year students.

Interim Assessment

• Interim assessment (2 module)
  0.1 * home assignments + 0.7 * December exam + 0.2 * Midterm test
• Interim assessment (4 module)
  0.1 * home assignments + 0.5 * Final exam + 0.4 * Interim assessment (2 module)

Bibliography

Recommended Core Bibliography

• Applied econometric time series, Enders, W., 2004
• Elements of forecasting, Diebold, F. X., 2007

Recommended Additional Bibliography

• Analysis of financial time series, Tsay, R. S., 2005
• Elements of financial risk management, Christoffersen, P. F., 2012