University of Piraeus. M.Sc. in Banking and Finance

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1 University of Piraeus M.Sc. in Banking and Finance Financial Derivatives Course Outline (January 2009) George Skiadopoulos, Ph.D. University of Piraeus, Department of Banking and Financial Management Financial Options Research Centre, University of Warwick Στο πλαίσιο και κατ εφαρμογή των διατάξεων των ν. 2387/20, 4301/29, του ν.δ. 3565/56, 4254/62, 4264/62 και ν. 100/75, ν. 2121/93, απαγορεύεται χωρίς γραπτή άδεια του Φυσικού Προσώπου με την επωνυμία Γεώργιος Σκιαδόπουλος, η αναδημοσίευση και γενικά η αναπαραγωγή με οποιοδήποτε μέσο ή τρόπο, μηχανικό, ηλεκτρονικό, φωτοτυπικό, ηχογράφησης ή άλλως πως, τμηματικά ή περιληπτικά στο πρωτότυπο ή σε μετάφραση, κατά παράφραση ή διασκευή, του συνόλου των παρόντων σημειώσεων που φέρουν την ένδειξη «Copyright 2006, Dr. George Skiadopoulos» σε κάθε σελίδα. Το παρόν έντυπο αποτελεί πνευματική ιδιοκτησία και copyright του Γεωργίου Σκιαδόπουλου.

2 Duration: 30 hours- 3 hours lecture, once a week (18:00-21:00). Objective This course aims to make students familiar with the financial derivatives; particular attention will be paid to pricing and hedging issues. Index futures and swaps will be analysed. Static and dynamic hedging techniques shall be discussed, and the Black- Scholes and the binomial model will be presented. Monte Carlo simulation shall be explained. Alternative to Black-Scholes models will be presented as well as options on futures and currencies. Audience The course is designed for those who aim to participate (or already participating) in the Greek and international derivatives markets as traders, research analysts, or fund managers. It will also be helpful to prospective doctoral students. Preliminaries The course does not assume prior knowledge of derivatives instruments. It will start from basic concepts and it will move fast to more advanced. Use of mathematics will be done when necessary, but they will be explained thoroughly. It is desirable that students be familiar with basic finance, and calculus/ statistics concepts (e.g. Present Value, arbitrage, types of interest rates, partial derivatives, probability distribution, expected value, variance). Examination Students will be marked according to their performance on the group assignments (GA), and on a three hours final exam (FE). The group assignments will contribute to the 15% of the final mark (FM), provided that the mark in the final exam is greater than five (5). Hence, FM=15% GA + 85% FE The group assignments will cover all the taught sections. Their purpose is to facilitate the students understand the lectures. Some of the exercises will be implemented in Excel, while the multiple choice questions will be similar to those set in the final exam. The evaluation process has been designed so that to reward the hard workers and penalize the free riders. Note: Students are urged to read the chapters listed on the next page before each class. Further readings will be assigned from time to time. Students are also urged to learn a spreadsheet program such as Microsoft Excel. 2

3 Bibliography The Lecture s notes will be distributed. These draw on material from the course textbooks and the recommended references. Course Outline The course will cover the following Sections: Section 1: Index Futures. Section 2: Swaps. Section 3: Introduction to Options. Section 4: Price Factors & Arbitrage Bounds Section 5: Binomial Trees. Section 6: The Black-Scholes model. Section 7: Risk Management and Dynamic Hedging. Section 8: Mathematical Approaches to Option Pricing. Section 9: Index, Currency and Futures Options. Section 10: Monte Carlo Simulation. Section 11: Alternative Models to Black-Scholes. [4 hours] 3

4 Course Textbook Hull, J. (2008). Options, Futures and other Derivatives, Prentice Hall, 7th Edition. Recommended References General Other textbooks Rubinstein M. (1999). Derivatives: A PowerPlus Picture Book. Volume 1: Futures, Options and Dynamic Strategies (see also Web site of Berkeley s University). Numerical Methods: Clewlow, L. and Strickland, C. (1998). Implementing Derivatives Models, John Wiley Wilmott, P (2001). Paul Wilmott Introduces Quantitative Finance, John Wiley Mathematical Approaches to Option Pricing Dothan, M.(1990). Prices in Financial Markets, Oxford University Press. Oksendal, B. (1991). Stochastic Differential Equations, 3 rd Edition, Springer Verlag Neftci, S. (2000). An Introduction to the Mathematics of Financial Derivatives, 2 nd Edition, Academic Press. Black-Scholes Model Black, F., and Scholes, M. (1973). The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81, pp Merton, R. C. (1974). The Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance, 29, pp Options and Risk Management Connolly, K. (1997). Buying and Selling Volatility, Wiley Editions. Natenberg, S. (1994). Option Volatility & Pricing: Advanced Trading Strategies and Techniques, Irwin Professional Publishing. Psychoyios, D., and Skiadopoulos, G. (2006): Volatility Options: Hedging Effectiveness, Pricing, and Model Error, Journal of Futures Markets, 26, pp Binomial Trees Chriss, N. (1997). Black Scholes and Beyond, McGraw-Hill. Cox, J., Ross, S., and Rubinstein, M. (1979). "Option Pricing: A Simplified Approach", Journal of Financial Economics, 7, pp Hull, J. and A. White (1988) The use of Control Variate Technique in Option Pricing, Journal of Financial and Quantitative Analysis, 23, pp

5 Mathematical Approaches to Option Pricing Dothan, M. (1990). Prices in Financial Markets, Oxford University Press. Oksendal, B. (1991). Stochastic Differential Equations, 3 rd Edition, Springer Verlag Neftci, S. (2000). An Introduction to the Mathematics of Financial Derivatives, 2 nd Edition, Academic Press. Options on Stock Indices, Currencies and Futures Black, F., and Scholes, M. (1973). The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81, pp Black, F. (1976). The Pricing of Commodity Contracts, Journal of Financial Economics, 3, pp Garman, B and Kohlhagen, S. (1983). Foreign Currency Option Values, Journal of International Money and Finance, 2, pp Merton, R. (1973). Theory of Rational Option Pricing, Bell Journal of Economics and Management Science, 4, pp Monte Carlo Simulation Boyle, P. (1977). Options: a Monte Carlo approach. Journal of Financial Economics, 4, pp Boyle, P., Broadie, and Glasserman (1997). Monte Carlo Methods for Security Pricing, Journal of Economic Dynamics and Control 21, pp Campbell, J., Lo, A. and MacKinlay, A (1997). The Econometrics of Financial Markets, Princeton University Press. Kritzman, M. (1993). About Monte Carlo Simulation, Financial Analysts Journal 49, 6, pp Paskov, S. and Traub, J. (1995). Faster Valuation of Financial Derivatives, Journal of Portfolio Management, pp Vose, D. (1997). Quantitative Risk Analysis: A Guide to Monte Carlo Simulation Modeling. John Wiley. Volatility Figlewski, Stephen (1997). Forecasting Volatility, Financial Markets, Institutions & Instruments 6, New York University Salomon Center. Skiadopoulos, George, Hodges, Stewart, and Clewlow, Les (1999). The Dynamics of the S&P 500 Implied Volatility Surface, Review of Derivatives Research 3, Alternatives to Black Scholes Derman, E. and Kani, I. (1994), Riding on a smile, Risk 7, pp Hull, J. and White, A. (1987). The Pricing of Options on Assets with Stochastic Volatilities, Journal of Finance, 42, pp

6 Merton, R. (1976). Option Pricing when Underlying Stock Returns are Discontinuous, Journal of Financial Economics, 3, pp Ledoit, O. and Santa-Clara, P. (1998), Relative Pricing of Options with Stochastic Volatility, Working Paper, University of California, Los Angeles. Panigirtzoglou, Ν., and Skiadopoulos, G. (2004): A New Approach to Modeling the Dynamics of Implied Distributions: Theory and Evidence from the S&P 500 Options, Journal of Banking and Finance, 28:7, pp Skiadopoulos, G. (2001): Volatility Smile Consistent Option Models: A Survey, International Journal of Theoretical and Applied Finance 4:3, pp Skiadopoulos, G., and Hodges, S. (2001): "Simulating the Evolution of the Implied Distribution", European Financial Management Journal, 7:4, pp Psychogios, D., Skiadopoulos, G., and Alexakis, P. (2003): A Review of Stochastic Volatility Processes: Properties and Implications, Journal of Risk Finance 4:3, pp About the Lecturer Dr. George Skiadopoulos is Assistant Professor in Financial Derivatives in the Department of Banking and Financial Management of the University of Piraeus. He is also an Associate Research Fellow at the Financial Options Research Centre (FORC) of the University of Warwick. He graduated from the Athens University of Economics and Business (best grade in his graduation class) and holds a Ph.D. in Financial Derivatives from the University of Warwick, and an M.Sc. in Econometrics and Mathematical Economics from the London School of Economics. From 1995 to 1999 he was a Research Fellow at FORC undertaking projects for corporate members of the centre. In the period , he worked in the R&D Group of the Athens Derivatives Exchange (ADEX). In 2003, he consulted ADEX to develop pricing models for volatility derivatives and an implied volatility index for the Greek market. He has also acted as a consultant to Greek and international financial institutions and has taught in many executive training seminars in Athens, London, and Barcelona. He has published in academic journals, in edited book volumes, and is a speaker in international conferences for academics and practitioners. He serves in the editorial board of the Journal of Business Finance and Accounting and is a member of the Academic Advisory Council of the Professional Risk Managers International Association (PRMIA). His research and teaching interests lie in the areas of option pricing and hedging, risk management, alternative investments, & portfolio management. For more information please visit 6