Course Outline (preliminary) Derivatives Pricing

Transcription

1 ADMI 841 Winter 2017 Tu MB S2.105 Professor Stylianos Perrakis Concordia University, MB Phone: Office hours: Wednesday , and by appointment Course Outline (preliminary) Derivatives Pricing This course is addressed to PhD and M.Sc. students who have an interest in doing research work on the general topic of option pricing. It provides an advanced coverage of the general theory of derivatives pricing, and an examination of some special topics within option pricing and financial engineering that can stimulate the selection of research topics for advanced degrees in finance and mathematics. It focuses primarily on theory, but it also includes some special topics and empirical applications. It can be extended or modified to accommodate the interests of the students taking the course, who will be encouraged to bring to the class the problems they are concerned with. Students taking this course are expected to be already familiar with the basics of options and futures as covered in Investments courses or undergraduate Futures and Options courses, as in the first part of the textbooks by Ritchken and Hull. In other words, they should be familiar with futures and options and futures and options markets, with option strategies and the arbitrage bounds, and with an elementary treatment of the binomial and Black-Scholes models. Depending on the level of preparation of the class, there will be refresher sessions for the required topics at the beginning of the course. Familiarity with stochastic calculus is helpful but is not required, since the relevant elements will be presented during the course.

2 Part of the course will be covered by the instructor and part will be given as a seminar. The course starts with the introduction of a few basic notions such as complete markets and elements of continuous time finance like the Wiener process. It then includes the basic models in option pricing, based on the absence of arbitrage, at a rather theoretical level. There will be problems all along this part of the course, whose solutions will be posted in the class folder. The course will then proceed to the more interesting cases, where the basic models fail. These are the cases of violations of the fundamental assumptions of the basic model, market completeness and frictionless trading. Derivatives pricing models in the presence of market incompleteness will be examined, principally those including stochastic volatility and jump processes; in these models absence of arbitrage is supplemented by market equilibrium considerations. The attempts to deal with the presence of market frictions such as transaction costs will also be documented, demonstrating the failure of the basic model to accommodate them. In parallel with the basic models the course will examine the stochastic dominance approach to option pricing. This approach was originally developed to deal with market incompleteness. It has been extended to include option pricing in the presence of proportional transaction costs. Recent contributions have demonstrated the links of this approach with the basic model and introduced new empirical methods based on the theoretical insights that it provides. In the part of the course that will be given as a seminar one or two students are supposed to select one of the indicated groups of articles (depending on size and difficulty) dedicated to one theme from among those starred in the bibliography. 1 Other articles or themes may be substituted with the consent of the instructor if there is particular interest on the part of a student, provided they are deemed relevant to the topic of the course. 2 The article selection should be completed by the fourth week of class, namely January 31, 2017, at which time the final class schedule will be formulated. For every group of articles the student must present it to the class, and lead the subsequent discussion. The student presentations will be interspersed with those of the instructor. Depending on the group, the presentations will take from one half to a full class session. If two students work together their individual work and presentations should be clearly identifiable. The student(s) will also draft a critical summary of the articles presented in the form of literature review. The students are also expected to write a research paper on a topic covered or related to the contents of the course, and present their work to the class at the end of the course. The research paper could possibly lead to a thesis plan. A number of topics will be suggested at the beginning of the course. Performance in the course is evaluated as follows: 1 The non-starred articles will generally be covered by the instructor. 2 Examples of such themes are option market microstructure, employee stock options, behavioral models of option pricing, or warrants and convertible bonds.

3 Article presentations 25% Exam 30% Project 45% Notes: 1. The topic of derivatives pricing has a heavy mathematical content by its own nature. While such use of mathematics cannot be avoided, a major effort will be expended in simplifying the presentation and avoid reliance on advanced mathematical concepts. We are more interested in economic intuition and results that are useful in practical or empirical applications, rather than in economic rigor. 2. The packaging of the topics follows research trends in front line journals. Some of the groupings, for instance the division between theoretical option models and empirical evidence, were done on historical guidelines; the more recent trend is to include both theory and empirical work within the same study. Textbooks (recommended-readings or problems to be assigned from) J. C. Cox and M. Rubinstein, Option Markets, Prentice Hall, 1985 (CR). D. Duffie, Dynamic Asset Pricing Theory, 3 rd edition, Princeton University Press, 2001 (D) J. C. Hull, Options, Futures, and Other Derivatives, 9 th edition, Prentice Hall, 2014 (H). D. Luenberger, Investment Science, Oxford University Press, 1998 (L). R. Merton, Continuous Time Finance, Blackwell Publishing Ltd., 1992 (M). P. Ritchken, Derivative Markets, Harper Collins, 1996 (R). C.S. Tapiero, Applied Stochastic Models and Control for Finance and Insurance, Kluwer Academic Press, 1998 (T). Preliminary course topics and schedule Note: In the outline below the indicated number of lectures refers to the presentations by the instructor. The time devoted to the topic will, of course, depend on the articles chosen for student presentations in each case, from the group of starred articles shown in each topic. The list of starred articles is intended only as suggestive and is nonexclusive. The relative length of the time devoted to the various parts of the course will depend on class preparation.

4 1. Introduction to the course. Brief review of derivative instruments, options and futures. Arbitrage relations and properties of option prices. Complete and incomplete markets. Discrete or continuous time models. The basic models: binomial and Black-Scholes option models derived with an elementary approach. The pricing kernel and the Black-Scholes model as an equilibrium model. (1-2 lectures). CR ch. 4; R ch. 6, 8, 9; D ch. 1, 2; H, ch. 11, 12, 13; L, ch. 13 Bergman, Y. Z., B. Grundy and Z. Wiener, (1996), Generalized Properties of Option Prices, Journal of Finance, 51, R. Merton, Theory of Rational Option Pricing, Bell Journal of Economics and Management Science 4 (Spring 1973), H. Varian (1987), The Arbitrage Principle in Financial Economics, The Journal of Economic Perspectives, Brennan, M. J. (1979), The Pricing of Contingent Claims in Discrete Time Models. Journal of Finance, 34, 1, Rubinstein, M. (1976), The Valuation of Uncertain Income Streams and the Pricing of Options, Bell Journal of Economics, 7, 2, Introduction to continuous time finance. Stochastic processes, random walks, Ito s lemma and the lognormal distribution. Rare events and jump processes. Applications to option pricing in complete markets (1-2 lectures). Options with non-standard payoffs and generalized diffusion models. Applications of the arbitrage method to term structure of interest rates models. M, ch. 3, 8; R, ch. 7; H, ch. 14, 15, 29, 31; T, ch. 2, 3; L, ch. 11. Article group: The CEV option pricing *Beckers, S., (1980), The Constant Elasticity of Variance Model and its Implications for Option Pricing, Journal of Finance, 35, *Cox, J., and S. Ross, The valuation of options for alternative stochastic processes, Journal of Financial Economics 3, *Emanuel, D., and MacBeth, J., Further results on the constant elasticity of variance call option pricing model, Journal Financial and Quantitative Analysis, 17,

5 *Geske, R., (1979), The Valuation of Compound Options, Journal of Financial Economics, 7, *Schroder, M., Computing the constant elasticity of variance option pricing formula, Journal of Finance 44, Extensions of the basic model: the arbitrage equilibrium approach, and the P- and Q-distributions. Option pricing in incomplete markets: jump processes, GARCH and stochastic volatility. The pricing kernel and its properties. Extensions to other types of derivative instruments. Article group: Jump- diffusion option pricing *Amin, K (1993), Jump Diffusion Option Valuation in Discrete Time, Journal of Finance, 48, *Bates, D. S., 1988, Pricing Options Under Jump-Diffusion Processes, Working Paper 37-88, The Wharton School, University of Pennsylvania. * Bates, D. S. (1991), The Crash of 87: Was it Expected? The Evidence from Option Markets. Journal of Finance, 46, *Merton, R. (1976), Option Pricing When Underlying Stock Returns are Discontinuous. Journal of Financial Economics, 3, Article group: Stochastic volatility option pricing *Amin, K. I. and V. K. Ng (1993), Option Valuation With Systematic Stochastic Volatility, Journal of Finance, 48, *Bates, D. S., (1996), Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options. Review of Financial Studies, 9, *Heston, S. L., (1993), A Closed-Form Solution for Options with Stochastic Volatility, with Applications to Bond and Currency Options. Review of Financial Studies, 6, *Hull, J., and A. White (1987), The Pricing of Options on Assets with Stochastic Volatilities. Journal of Finance, 42, *Wiggins, J. (1987), Option Values Under Stochastic Volatility: Theory and Empirical Estimates. Journal of Financial Economics, 5, Article group: GARCH option pricing

6 *Christoffersen, P., Heston, S., and K. Jacobs, 2013, Capturing Option Anomalies with a Variance-Dependent Pricing Kernel, Review of Financial Studies, 26, *Duan, Jin-Chuan (1995), The GARCH Option Pricing Model. Mathematical Finance, 5, *Heston, S. L., and S. Nandi, (2000), A Closed-form GARCH Option Valuation Model. Review of Financial Studies, 13, Article group: Variance swaps and volatility trading *Britten-Jones, M., and A. Neuberger, 2000, Option Prices, Implied Price Processes and Stochastic volatility, Journal of Finance 55, *Carr, P., and L. Wu, (2009), Variance Risk Premiums, Review of Financial Studies, 22, *Jiang, G. J., and Y. Tian, 2005, The Model-Free Implied Volatility and its Information content, Review of Financial Studies 18, The basic model under transaction costs. Option replication in the Black-Scholes and binomial models. The expected utility approach. Article group: Replication *Boyle, P. P. and T. Vorst, Option Replication in Discrete Time with Transaction Costs. Journal of Finance 47, *Leland, H. E., Option Pricing and Replication with Transactions Costs. Journal of Finance 40, *Merton, R.., On the Application of the Continuous-time Theory of Finance to Financial Intermediation and Insurance. The Geneva Papers on Risk and Insurance 14, Article group: Super replication *Bensaid, B., J-P. Lesne, H. Pagés and J. Scheinkman, 1992, Derivative Asset Pricing with Transaction Costs. Mathematical Finance 2, *Perrakis, S., and J. Lefoll, Option Pricing and Replication with Transaction Costs and Dividends, Journal of Economic Dynamics and Control, November 2000.

7 *Perrakis, S., and J. Lefoll The American Put Under Transaction Costs, Journal of Economic Dynamics and Control, February The empirical failure of the basic model. The volatility smile. Implied distributions and alternative explanations of the smile. Extracting the P- and Q- distributions from the underlying and the option markets. Equity options Jackwerth, J. C., (2004), Option-implied risk-neutral distributions and risk aversion, ISBN , Research Foundation of AIMR, Charlottesville, USA. I. Index and futures options Article group: Extracting the Q-distribution from options *Ait-Sahalia, Y., and A. W. Lo, Nonparametric Estimation of State-Price Densities Implied in Financial Asset Prices, Journal of Finance, 53, 2, *Bakshi, G., C. Cao and Z. Chen, Empirical Performance of Alternative Option Pricing Models. The Journal of Finance, 52, * Buraschi, A., and J. Jackwerth (2001), The Price of a Smile: Hedging and Spanning in Option Markets, Review of Financial Studies, 14, *Dumas, B., J. Fleming, and R. Whaley, Implied Volatility Functions: Empirical Tests. The Journal of Finance, 53, *Ioffe, I. D., and E. Prisman, 2013, Arbitrage Violations and Implied Valuations: the Option Market, European Journal of Finance 19, *Jackwerth, C., and M. Rubinstein, Recovering Probability Distributions from Option Prices, Journal of Finance, 51, *Rubinstein, M., Implied Binomial Trees, Journal of Finance, 49, 3, Article group: Reconciling the P- and Q-distributions *Ait-Sahalia, Yashin, 2004, Disentangling Diffusion from Jumps, Journal of Financial Economics, 74, *Bliss, R., and N. Panigirtzoglou, Option-Implied Risk Aversion Estimates, Journal of Finance, 59,

8 *Christoffersen, P., Elkamhi, R., Feunou, B., & Jacobs, K. (2010). Option valuation with conditional heteroskedasticity and nonnormality. Review of Financial Studies, 23(5), *Christoffersen, P., Jacobs, K., & Mimouni, K. (2010). Volatility dynamics for the S&P500: Evidence from realized volatility, daily returns, and option prices. Review of Financial Studies, 23(8), *Eraker, B., M. Johannes and N. Polson, 2003, The Impact of Jumps in Volatility and Returns, Journal of Finance, 58, *Jackwerth, J., (2000). Recovering Risk Aversion from Option Prices and Realized Returns, Review of Financial Studies, 13, *Rosenberg, J. V., and R. F. Engle, 2002, Empirical Pricing Kernels, Journal of Financial Economics, 64, II. Equity options Article group: Equity options, theory and empirical research *Bakshi, G., N. Kapadia and D. Madan (2003), Stock Return Characteristics, Skew Laws and the Differential Pricing of Individual Equity Options Review of Financial Studies, 16, *Bollen, N. P., and R. Whaley, 2004, Does Net Buying Pressure Affect the Shape of Implied Volatility Functions?, Journal of Finance 59, *Driessen, J., P. J. Maenhout, and G. Vilkov, 2009, The Price of Correlation Risk: Evidence from Equity Options, Journal of Finance 64, *Duan, Jin-Chuan, and Jason Wei (2009), Systematic Risk and the Price Structure of Individual Equity Options. Review of Financial Studies, 22, *Goyal, A., and A. Saretto, (2009) Cross-section of option returns and volatility, Journal of Financial Economics 94, Article group: Option-implied betas *Boloorforoosh, Ali, Is idiosyncratic volatility priced? Evidence from the physical and risk-neutral distributions, Working paper, Concordia University. *Buss, A. and G. Vilkov, Measuring equity risk with option-implied correlations. Review of Financial Studies 25 (10),

9 *Chang, B-Y., P. Christoffersen, K. Jacobs, and G. Vainberg, Optionimplied measures of equity risk, Review of Finance 16, *Christoffersen, P., M. Fournier, and K. Jacobs, The factor structure in equity options. Working Paper, University of Toronto. 6. Stochastic dominance option pricing I: Incomplete frictionless markets in discrete and continuous time. The monotonicity condition and option bounds. The linear programming approach. The Lindeberg condition and the convergence to continuous time, (1-2 lectures). Article group: Stochastic dominance in the absence of frictions: option bounds in discrete time *Bizid, A. and E. Jouini, Equilibrium Pricing in Incomplete Markets. Journal of Financial and Quantitative Analysis 40, *Grundy, B., Option Prices and the Underlying Asset s Return Distributions, Journal of Finance 46, *Levy, H., Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach. Journal of Finance 40, Perrakis, S. and P. J. Ryan, Option Pricing Bounds in Discrete Time. Journal of Finance 39, *Perrakis, S., Option Bounds in Discrete Time: Extensions and the Pricing of the American Put. Journal of Business 59, *Ritchken, P. H., On Option Pricing Bounds. Journal of Finance 40, *Ritchken, P.H. and S. Kuo, Option Bounds with Finite Revision Opportunities. Journal of Finance 43, Article group: Stochastic dominance in the absence of frictions: convergence of option bounds to continuous time *Oancea, I. M., and S. Perrakis, From Stochastic Dominance to Black Scholes: An Alternative Option Pricing Paradigm, Risk and Decision Analysis 5, *Ghanbari, H., Oancea, I. M., and S. Perrakis, Jump-Diffusion Option Valuation and Option-Implied Investor Preferences: a Stochastic Dominance Approach. Working Paper, Concordia University.

10 *Perrakis, S., and A. Boloorforoosh, Valuing catastrophe derivatives under limited diversification: a stochastic dominance approach, Journal of Banking and Finance 37, Perrakis, S., and A. Boloorforoosh, Catastrophe futures and reinsurance contracts: an incomplete markets approach, working paper, Concordia University. *Ross, S., The recovery theorem, Journal of Finance 70, Ryan, P. J., Progressive Option Bounds from the Sequence of Concurrently Expiring Options. European Journal of Operational Research 151, Stochastic dominance option pricing II: Transaction costs and option pricing bounds. Empirical implications, (1-2 lectures). Article group: Stochastic dominance under proportional transaction costs: theory and empirical applications *Constantinides, G. M., Jackwerth, J. C., and S. Perrakis, Option pricing: real and risk-neutral distributions, in J. R. Birge and V. Linetsky, Financial Engineering, Handbooks in Operations Research and Management Science, Elsevier/North Holland, *Constantinides, G. M., Jackwerth, J. C., and S. Perrakis, Mispricing of S&P 500 Index Options. Review of Financial Studies, 22, *Constantinides, G. M., Czerwonko, M., Jackwerth, J. C., and S. Perrakis, Are Options on Index Futures Profitable for Risk Averse Investors? Empirical Evidence. Journal of Finance 66, Constantinides, G. M., Czerwonko, M., and S. Perrakis, Mispriced option portfolios, working paper, University of Chicago and Concordia University. *Constantinides, G. M., and S. Perrakis, Stochastic Dominance Bounds on Derivatives Prices in a Multiperiod Economy with Proportional Transaction Costs, Journal of Economic Dynamics and Control, 26, *Constantinides, G. M., and S. Perrakis, "Stochastic Dominance Bounds on American Option Prices in Markets with Frictions." Review of Finance 11,

11 *Perrakis, S. and M. Czerwonko, Can the Black-Scholes-Merton Model Survive Under Transaction Costs? An Affirmative Answer. Working Paper, Concordia University. 8. The Option Model and the Valuation of Corporate Securities: Structural Models of Credit Instruments. Article group: Structural models of the firm (theory) *Colin-Dufresne, P., and R. S. Goldstein, 2001, Do Credit Spreads Reflect Stationary Leverage Ratios?, Journal of Finance 56, *Goldstein, R., N. Ju and H. Leland (2001). "An EBIT-based Model of Dynamic Capital Structure", Journal of Business, 74, *He, Z., and W, Xiong, Rollover Risk and Credit Risk, Journal of Finance 67, *Leland, H. E. (1994), Corporate Debt Value, Bond Covenants, and Optimal Capital Structure, Journal of Finance, 49, *Leland, H. (1998), Agency Costs, Risk Management, and Capital Structure, Journal of Finance, 53, *Leland, H. E., and K. B. Toft (1996), Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads, Journal of Finance, 51, *Zhou, C., 2001, The Term Structure of Credit Spreads with Jump Risk, Journal of Banking and Finance 25, Article group: Structural models of the firm (empirical applications) *Ericsson, J., K. and J. Reneby. (2005), Estimating Structural Bond Pricing Models, Journal of Business, 78, *Eom, Y., J. Helwege, and J. Huang. (2004), Structural Models of Corporate Bond Pricing: An Empirical Analysis, Review of Financial Studies, 17, *Huang, J. Z., and M. Huang, (2012), How Much of the Corporate-Treasury Yield Spread is Due to Credit Risk?, Review of Asset Pricing Studies 2, *Perrakis, S., and R. Zhong, (2015). Credit spreads and state-dependent volatility: Theory and empirical evidence, Journal of Banking and Finance 55,

12 Article group: Structural models of the firm and credit default swaps (empirical applications) *Kryzanowski, L., S. Perrakis and R. Zhong, 2016, Financial oligopolies: theory and empirical evidence from the Credit Default Swap Markets, working paper, Concordia University. *Schweikhard, F. A., and Z. Tsesmelidakis, The Impact of Government Intervention on CDS and Equity Markets, Working Paper, Goethe University. *Zhang Y., Zhou H., and Zhu H., 2009, Explaining credit default swap spreads with the equity volatility and jump risks of individual firms, Review of Financial Studies 22, Longstaff, F. A., and E. S. Schwartz (1995), A Simple Approach to Valuing Fixed and Floating Rate Debt, Journal of Finance, 50, Merton, R. C. (1974), On the Pricing of Corporate Debt: the Risk Structure of Interest Rates, Journal of Finance, 29, Sarkar, S., and F. Zapatero, 2003, "The Trade-Off Model with Mean-Reverting Earnings: Theory and Empirical Tests", Economic Journal, 115, Schaefer, S.M., and Strebulaev, I. A., 2008, Structural models of credit risk are useful: evidence from hedge ratios on corporate bonds, Journal of Financial Economics 90, Titman, S., and S. Tsyplakov, 2007, A Dynamic Model of Optimal Capital Structure, Review of Finance 11, Toft, K. B., and B. Prucyk (1997), Options on Leveraged Equity: Theory and Empirical Tests, Journal of Finance, 52, Project presentations (if there is time). 10. Exam (take home, at the end of the class). 11. Term paper (due approximately two months after the end of classes).