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Магистратура 2019/2020

Производные финансовые инструменты

Статус: Курс по выбору (Финансовая экономика)
Направление: 38.04.01. Экономика
Когда читается: 2-й курс, 1 семестр
Формат изучения: без онлайн-курса
Прогр. обучения: Финансовая экономика
Язык: английский
Кредиты: 3
Контактные часы: 48

Course Syllabus


The objective of Part 1 of the course is to undertake a rigorous study of derivative financial instruments. The course is quantitatively oriented and requires some background in calculus and statistics. Derivative financial instruments are instruments whose value is “derived” from the value of some underlying asset or assets. Our goal is to learn how to price such instruments using a noarbitrage principle, and how to hedge them. The course will be particularly relevant to students interested in financial markets, securities trading and structured products development involving derivatives. At the end of Part 1, my hope is that students will obtain two types skills. First, students will know key properties of standard derivative instruments, such as forwards, futures, swaps, and call and put options. Second, students will be comfortable with analyzing new derivative products using the techniques presented in class. Part 2 will provide a thorough understanding of the applications to which derivative securities can be put in modern financial markets. It will cover the operational characteristics of the instruments and the infra-structure in which they operate. The course will start with a review of the major derivative exchanges and an overview of the instruments offered and a distinction will be drawn between Exchange-based and off-exchange instruments. The course will examine some of the applications to which stock and index equity futures and options can be put and will also examine single and multi-period hedging of interest rates. Towards the end of the course participants will be introduced to asset swaps, total return swaps, credit default swaps and financially engineered equity products. Prerequisites: Financial Economics 1, intermediate calculus, probability theory
Learning Objectives

Learning Objectives

  • At the conclusion of the course, the students are expected to acquire the following skills: Ability to create new theories, invent new ways and tools of professional activity.
  • Ability to analyze, verify, evaluate the completeness of information in the course of professional activities, if necessary, to fill and synthesize the missing information.
  • Ability to develop strategies for the behavior of economic agents in different markets
  • Ability to present the results of the study to the scientific community in the form of an article or report
  • Ability to carry out applied and / or fundamental research, using advanced methods of economic analysis, including instrumental
Expected Learning Outcomes

Expected Learning Outcomes

  • distinguish between main derivative instruments and different types of options.
  • find an option price through binomial pricing.
  • find an option price using Black-Scholes approach.
  • find an option price under multiple sources of uncertainty.
  • apply Structural and reduced-form approach to credit risk modelling to calculate default probabilities
  • explain main differences between the different types derivatives and understand their nature, outline how the OTC derivatives work.
  • construct a replicating portfolio
  • do bond hedging with bond futures
  • be able to use difference between conversion factors for calculations
  • to construct swap contract for a given position of a firm
  • calculate returns on particular structured products
Course Contents

Course Contents

  • Fundamentals of derivative pricing: Overview
    Historical background and milestones in the development of derivative markets Key concepts: replication, underlying security, no arbitrage, relative versus absolute pricing Popular derivative instruments: forwards, futures, options
  • Option pricing: static and discrete-time analysis
    No arbitrage bounds on option prices. Types of options: European, American, Bermudan, Asian, etc. Binomial option pricing models: building binomial trees, pricing on the tree, risk neutral tree probabilities
  • Option pricing in continuous time
    Mathematics of option pricing: Brownian motion, Ito’s processes, Ito’s lemma, partial differential equations, martingale approach Pricing and replication in continuous time, Black-Scholes formula, option greeks, Empirical evaluation of Black-Scholes formula, volatility smile
  • Pricing with multiple sources of uncertainty
    Traded and non-traded risks, stochastic volatility and stochastic interest rate models, market price of risk, pricing convertible bonds
  • Structural and reduced-form models of credit risk
    Defaultable bonds, bond as an option, credit rating, risky yield curve
  • Exchange-based and OTC derivatives
    Exchange-based derivatives (ETDs): Futures and options – contract specifications, operational characteristics. Over-the-counter (OTC) derivatives: Forwards, Options. Hedging an equity portfolio with futures. Exchange Trade Funds (ETFs), Universal Stock futures (USFs and SSFs), speculation, arbitrage, ‘Chasing alpha’. Portfolio engineering using exchange-traded futures. OTC short term equity swaps (Contacts for Difference (CFD)). Option review.
  • Options and an introduction to Structured Certificates
    Market links between options and futures. Structuring certificates using options. The impact of time on officially recognised strategies.
  • Short Term interest Rates and Bonds
    Comparing FRAs and STIRs. Using STIR options and Interest Rate Guarantees to hedge single and multiple period exposures. Hedging using bond futures
  • Swaps
    Review of plain vanilla interest rate swaps. Some variations on the basic interest rate swap. Asset swaps. Total return swaps. Credit default swaps.
  • Structured Equity Products
    Constructing guaranteed principal products (GPP).
Assessment Elements

Assessment Elements

  • non-blocking test
    Students who missed the test due to a valid reason are assigned an additional date to sit it.
  • blocking Exam
  • non-blocking home assignments
Interim Assessment

Interim Assessment

  • Interim assessment (1 semester)
    0.53 * Exam + 0.17 * home assignments + 0.3 * test


Recommended Core Bibliography

  • Hull, J. C. (2017). Options, Futures, and Other Derivatives, Global Edition. [Place of publication not identified]: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1538007

Recommended Additional Bibliography

  • Paul Wilmott. (2013). Paul Wilmott on Quantitative Finance. [N.p.]: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=185503