Prof. Jakša Cvitanić, Department of Humanities and Social Sciences, California Institute of Technology

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1 Prof. Jakša Cvitanić, Department of Humanities and Social Sciences, California Institute of Technology September 14 th, 2015 Zagreb School of Economics and Management

2

3 COURSE OBJECTIVES: The objective of the course is to provide a systematic framework for understanding the role of financial derivatives, the methods for their valuation, and the use of those in risk management, starting from simple ones like futures and swaps, to more complicated, such as options. We will learn how to measure the risks and rewards associated with them, how they can add value to a firm, but also how they can lead to losses if used without sufficient understanding. We will also learn how to use derivatives to hedge different types of risks, including currency risk, real estate risk and risk of trading in commodities such as oil or gas. The modeling workhorse for this purpose is a simple binomial tree method of Cox, Ross and Rubinstein, which can be used to explain pricing of even the most complicated derivatives. This model will also enable us to understand the famous Black-Scholes model, and its extensions. Moreover, we will analyze the main factors driving the value of various derivatives, such as volatility for options on stocks, interest rates and forward rates for derivatives in the bond markets, and default probabilities and correlations for credit risk derivatives. WHO DO WE RECOMMEND TO ATTEND? The course will be highly useful to: senior executives of financial and non-financial firms, risk managers, bankers, investment managers, management consultants, analysts, corporate treasurers and regulatory officials.

4 Whether they have some familiarity with the complex world of derivatives, but want to learn more, or they want to have the first exposure to these topics, in a systematic and easy to build on fashion. Managers in all industries who make decisions on financial and risk/reward issues, whether it involves aspects of marketing, engineering or production, as well as corporate boards members will benefit from this course. The course assumes no prior knowledge of financial derivatives, while still leading to the advanced knowledge on the subject. PRIOR PREPARATION EXPECTED: The course will be structured in a self-contained way, so that no prior knowledge on the subject is required. However, some familiarity with basic statistics and probability is helpful for quicker understanding of the material and taking the full advantage of the course. AT THE END OF THE COURSE YOU SHOULD BE ABLE TO: understand what futures, swaps, and options are used for know their advantages and disadvantages have basic tools for valuing positions in derivatives understand which market factors influence those values understand the Black-Scholes formula know in which way prices of different instruments are connected value exchange rates based derivatives hedge financial market positions of a firm understand the effect of derivatives positions on downside risk vs. upside potential establish strategies consistent with your view on the future market behaviour measure and manage financial risks

5 ABOUT THE LECTURER: Jakša Cvitanić is a Richard N. Merkin Professor of Mathematical Finance at the California Institute of Technology, one of the top five universities in the world. He teaches options, interest rate and credit risk derivatives, mathematical finance and contract theory. In addition to regular university courses, he has taught several intensive courses, including, most recently, in academic year 2012/13, a course on derivatives for MBA students at EDHEC Business School, Nice, and previously in Johannesburg, Cape Town, Lausanne, Kyoto, Berlin, Paris, Hanoi, and Bressanone. His former students work as analysts at big Wall Street investment banks and other banks throughout the US and the world, as well as professors in Business Schools and Quantitative Finance programs. He has co-authored some fundamental papers on financial markets with portfolio constraints, transaction costs, and other market imperfections. Cvitanic is the author of over fifty articles published in top scholarly finance, economics and mathematics journals, and a co-author, with Fernando Zapatero, of the textbook Introduction to the Economics and Mathematics of Financial Markets, published by MIT Press. He is one of the co-editors of Finance and Stochastics and Mathematical Finance, and is on editorial boards of several other journals. Prior to joining Caltech in 2005, Cvitanic was a Professor of Mathematics and Economics at the University of Southern California, and before that, Assistant and Associate Professor of Statistics at Columbia University. He was awarded a Ph.D by Columbia University in New York in 1992.

6 THE COURSE STRUCTURE: Session 1 Part 1: Trading Futures, Forwards and Swaps. Using futures for hedging or for speculation. Hedging risk using futures. Part 2: Pricing Futures, Forwards and Swaps. Pricing these contracts on foreign currencies and commodities. Session 2 Part 1: Options fundamentals, Put-Call Parity. Exotic options. Static option strategies. Part 2: Options with early exercise, options on interest rates, real estate and credit risk derivatives. Session 3 Part 1: Black-Scholes Formula. Pricing options on dividend paying securities. Part 2: Option sensitivities ( greeks ), implied volatility. Session 4 Part 1: Computing option prices in a single-period Binomial Tree. Pricing by replication. Pricing by risk-neutral probabilities.: Multi-period trees, backward algorithm for pricing. American options. Part 2: Hedging option positions, delta hedging. Portfolio Insurance. RECOMMENDED READING Standard textbooks: Hull, J., 2009, Options, Futures and Other Derivatives, Prentice Hall. McDonald, R., 2006, Derivatives Markets, Pearson. Back, K. 2010, A Course in Derivative Securities.

7 Additional (more advanced) textbooks: Bjork, T., 2005, Arbitrage theory in continuous time, Oxford University Press. Cvitanic, J. and Zapatero, F. 2004, Introduction to the Economics and Mathematics of Financial Markets. MIT Press. Nielsen, L.T., 1999, Pricing and hedging of derivative securities, Oxford U. Press. Shreve, S., 2004, Stochastic calculus for finance II: continuous time models, Springer Finance. REGISTRATION INFORMATION: The program fee is 1.800,00 kn + PDV. The fee includes tuition, instructional materials, literature, lunch and reception. Number of seats on the seminar is limited. The deadline for registering is September 1 st, For our partners we have a special discount, FOR TWO paid fees, THIRD person can come for free. This offer is available until August 24 th, 2015.

8 CONTACT: Lana Mažuranić, MBA ZSEM Business Academy ltd. Phone: 01/ Fax: 01/

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