Course Outline (preliminary)



ADM 841J

Winter 2010

Tu. 14.00-17.00

MB 3.285

Professor Stylianos Perrakis

Concordia University, MB 12.305

Email: sperrakis@jmsb.concordia.ca

Phone: 514-848-2424-2963

Course Outline (preliminary)

Derivatives Pricing

This course is addressed to 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 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. One or two brief refresher sessions will be devoted to the required topics at the beginning of the course.

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, with which a basic familiarity is assumed. It then includes the basic models in option pricing, based on the absence of arbitrage, at a rather advanced 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 recently 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 students are supposed to select articles (at least two) or focus on a group of papers dedicated to one theme from among those starred in the bibliography. The article selection should be completed by the third week of class, namely January 19, 2010. For every article the student must present it to the class, and lead the subsequent discussion. The student presentations will be interspersed with those of the instructor.

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:

Article presentations 20%

Project presentation 10%

Exam 30%

Project 40%

Note: The topic of derivatives pricing has a heavy mathematical content by its own nature. While such heavy 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.

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, 3rd edition, Princeton University Press, 2001 (D)

J. C. Hull, Options, Futures, and Other Derivatives, 6th edition, Prentice Hall, 2006 (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 non-exclusive.

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, 13, 14; L, ch. 13

R. Merton, “Theory of Rational Option Pricing”, Bell Journal of Economics and Management Science 4 (Spring 1973), 141-84.

H. Varian (1987), “The Arbitrage Principle in Financial Economics”, The Journal of Economic Perspectives, 55-72.

Brennan, M. J. (1979), “The Pricing of Contingent Claimes in Discrete Time Models.” Journal of Finance, 34, 1, 53-68.

Rubinstein, M. (1976), “The Valuation of Uncertain Income Streams and the Pricing of Options”, Bell Journal of Economics, 7, 2, 407-425.

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 and incomplete markets (1-2 lectures). Options with non-standard payoffs and generalized diffusion models.

M, ch. 3, 8; R, ch. 7; H, ch. 12, T; ch. 2, 3; L, ch. 11.

*Beckers, S., (1980), “The Constant Elasticity of Variance Model and its Implications for Option Pricing”, Journal of Finance, 35, 661-673

*Bergman, Y. Z., B. Grundy and Z. Wiener, (1996), “Generalized Properties of Option Prices”, Journal of Finance, 51, 1573-1610.

*Geske, R., (1979), “The Valuation of Compound Options”, Journal of Financial Economics, 7, 63-81.

*Goldman, B. M., H. B. Sosin, and M. A. Gatto, (1979), “Path Dependent Options: Buy at the Low, Sell at the High”, Journal of Finance, 34, 1111-1128.

*Margrabe, W., (1978), “The Value of an Option to Exchange an Asset for Another”, Journal of Finance, 33, 177-186.

*Rubinstein, M. (1983), “Displaced Diffusion Option Pricing”, Journal of Finance, 38, 213-217.

3. Extensions of the basic model: option pricing in incomplete markets. Jump processes, GARCH and stochastic volatility.

*Amin, K (1993), “Jump Diffusion Option Valuation in Discrete Time”, Journal of Finance, 48, 1833-1863.

*Amin, K. I. and V. K. Ng (1993), “Option Valuation With Systematic Stochastic Volatility”, Journal of Finance, 48, 881-909.

*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, 101-143.

*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, 1009-1044.

*Bates, D. S., (1996), “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options.” Review of Financial Studies, 9, 69-107.

*Duan, Jin-Chuan (1995), “The GARCH Option Pricing Model.” Mathematical Finance, 5, 13-32.

*Duan, Jin-Chuan, and Jean-Guy Simonato (2001), “American option pricing under GARCH using a Markov chain approximation.” Journal of Economic Dynamics and Control 25, 1689-1718.

*Duan, Jin-Chuan, and Jason Wei (2009), “Systematic Risk and the Price Structure of Individual Equity Options.” Review of Financial Studies, 22, 1981-2006.

*Frey, R., and C. Sin, (1999), “Bounds on European Option Prices Under Stochastic Volatility”, Mathematical Finance, 97-116.

*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, 327-344.

*Heston, S. L., and S. Nandi, (2000), “A Closed-form GARCH Option Valuation Model.” Review of Financial Studies, 13, 585-625.

*Hull, J., and A. White (1987), The Pricing of Options on Assets with Stochastic Volatilities.” Journal of Finance, 42, 281-300.

*Merton, R. (1976), “Option Pricing When Underlying Stock Returns are Discontinuous.” Journal of Financial Economics, 3, 125-144.

*Ritchken, Peter, and R. Trevor (1999), “Pricing Options Under Generalized GARCH and Stochastic Volatility Processes.” Journal of Finance, 54, 377-402.

*Wiggins, J. (1987), “Option Values Under Stochastic Volatility: Theory and Empirical Estimates.” Journal of Financial Economics, 5, 351-372.

4. The basic model under transaction costs. Option replication in the Black-Scholes and binomial models. The expected utility approach.

*Bensaid, B., J-P. Lesne, H. Pagés and J. Scheinkman, 1992, “Derivative Asset Pricing with Transaction Costs.” Mathematical Finance 2, 63-86.

*Boyle, P. P. and T. Vorst, 1992. “Option Replication in Discrete Time with Transaction Costs.” Journal of Finance 47, 271-293.

*Constantinides, G. M. and T. Zariphopoulou, 1999. “Bounds on Prices of Contingent Claims in an Intertemporal Economy with Proportional Transaction Costs and General Preferences.” Finance and Stochastics, 3, 345-369

*Davis, M. H. A., V. G. Panas and T. Zariphopoulou, 1993. “European Option Pricing with Transaction Costs.” SIAM Journal of Control and Optimization 31, 470-493.

*Leland, H. E., 1985. “Option Pricing and Replication with Transactions Costs.” Journal of Finance 40, 1283-1301.

*Merton, R.., 1989. “On the Application of the Continuous-time Theory of Finance to Financial Intermediation and Insurance.” The Geneva Papers on Risk and Insurance 14, 225-261.

*Perrakis, S., and J. Lefoll, 2000. “Option Pricing and Replication with Transaction Costs and Dividends”, Journal of Economic Dynamics and Control, November 2000.

*Perrakis, S., and J. Lefoll 2004. “The American Put Under Transaction Costs”, Journal of Economic Dynamics and Control, February 2004.

*Zakamouline, V., 2006, “European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs,” Journal of Economic Dynamics and Control 30, 2006, 1-25.

5. The empirical failure of the basic model. The volatility smile. Implied distributions and alternative explanations of the smile.

Jackwerth, J. C., (2004), “Option-implied risk-neutral distributions and risk aversion”, ISBN 0-943205-66-2, Research Foundation of AIMR, Charlottesville, USA.

*Ait-Sahalia, Y., and A. W. Lo, 1998. “Nonparametric Estimation of State-Price Densities Implied in Financial Asset prices”, Journal of Finance, 53, 2 , 499-547.

*Bakshi, G., C. Cao and Z. Chen, 1997. “Empirical Performance of Alternative Option Pricing Models.” The Journal of Finance, 52, 2003-2049.

*Bliss, R., and N. Panigirtzoglou, 2004. “Option-Implied Risk Aversion Estimates”, Journal of Finance, 59, 407-446.

* Buraschi, A., and J. Jackwerth (2001), “The Price of a Smile: Hedging and Spanning in Option Markets”, Review of Financial Studies, 14, 495-527.

*Dumas, B., J. Fleming, and R. Whaley, 1998. “Implied Volatility Functions: Empirical Tests.” The Journal of Finance, 53, 2059-2106.

*Jackwerth, J., (2000). “Recovering Risk Aversion from Option Prices and Realized Returns”, Review of Financial Studies, 13, 433-451

*Jackwerth, C., and M. Rubinstein, 1996. “Recovering Probability Distributions from Option Prices”, Journal of Finance, 51, 1611-1631.

*Longstaff, F., 1995. “Option Pricing and the Martingale Restriction”, Review of Financial Studies, 8, 1091-1124.

*Masson, J., and S. Perrakis, 2000. “Option Bounds and the Pricing of the Volatility Smile”, Review of Derivatives Research, 4, 29-53.

*Rosenberg, J. V., and R. F. Engle, 2002, “Empirical Pricing Kernels,” Journal of Financial Economics, 64, 341-372.

*Rubinstein, M., 1994. “Implied Binomial Trees”, Journal of Finance, 49, 3, 771-818.

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).

*Bizid, A. and E. Jouini, 2005. “Equilibrium Pricing in Incomplete Markets.” Journal of Financial and Quantitative Analysis 40, 833-848.

*Grundy, B., 1991. “Option Prices and the Underlying Asset’s Return Distributions”, Journal of Finance 46, 1045-1069

*Levy, H., 1985. “Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach.” Journal of Finance 40, 1197-1217.

Oancea, I. M., and S. Perrakis, 2007. “Stochastic Dominance and Option Pricing in Discrete and Continuous Time: an Alternative Paradigm.” Working Paper, Concordia University.

*Oancea, I. M., and S. Perrakis, 2009. “Jump-Diffusion Option Valuation Without a Representative Investor.” Working Paper, Concordia University.

Perrakis, S., 1986. “Option Bounds in Discrete Time: Extensions and the Pricing of the American Put.” Journal of Business 59, 119-141.

* Perrakis, S., 1988. “Preference-free Option Prices when the Stock Return Can Go Up, Go Down, or Stay the Same.” Advances in Futures and Options Research 3, 209-235.

Perrakis, S. and P. J. Ryan, 1984. “Option Pricing Bounds in Discrete Time.” Journal of Finance 39, 519-525.

Ritchken, P. H., 1985. “On Option Pricing Bounds.” Journal of Finance 40, 1219-1233.

*Ritchken, P.H. and S. Kuo, 1988. “Option Bounds with Finite Revision Opportunities.” Journal of Finance 43, 301-308.

*Ryan, P. J., 2000. “Tighter Option Bounds from Multiple Exercise Prices.” Review of Derivatives Studies 4, No. 2, 155-188.

*Ryan, P. J., 2003. “Progressive Option Bounds from the Sequence of Concurrently Expiring Options.” European Journal of Operational Research 151, 193-223.

7. Stochastic dominance option pricing II: Transaction costs and option pricing bounds. Empirical implications, (1-2 lectures).

*Constantinides, G. M., Jackwerth, J. C., and S. Perrakis, 2007. “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, 565-591.

*Constantinides, G. M., Jackwerth, J. C., and S. Perrakis, 2009. “Mispricing of S&P 500 Index Options.” Review of Financial Studies, 22, 1247-1277.

*Constantinides, G. M., Czerwonko, M., Jackwerth, J. C., and S. Perrakis, 2008. “Are Options on Index Futures Profitable for Risk Averse Investors? Empirical Evidence.” Working Paper, University of Chicago.

*Constantinides, G. M., and S. Perrakis, 2002. “Stochastic Dominance Bounds on Derivatives Prices in a Multiperiod Economy with Proportional Transaction Costs,” Journal of Economic Dynamics and Control, 26, 1323-1352.

*Constantinides, G. M., and S. Perrakis, 2007. "Stochastic Dominance Bounds on American Option Prices in Markets with Frictions." Review of Finance 11, 71-115.

*Perrakis, S. and M. Czerwonko, 2009.“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.

*Ericsson, J., K. and J. Reneby. (2005), “Estimating Structural Bond Pricing Models”, Journal of Business, 78, 707-736.

*Eom, Y., J. Helwege, and J. Huang. (2004), “Structural Models of Corporate Bond Pricing: An Empirical Analysis”, Review of Financial Studies, 17, 499-544.

*Goldstein, R., N. Ju and H. Leland (2001). "An EBIT-based Model of Dynamic Capital Structure", Journal of Business, 74, 483-512.

*Hackbarth, D., J. Miao, and E. Morelle. (2007), “Capital Structure, Credit Risk and Macroeconomic Conditions”, Journal of Financial Economics, 82, 519-550.

*Ju, N., R. Parrino, A. Poteshman, and M. Weisbach. (2005), “Horses and Rabbits? Trade-off Theory and Optimal Capital Structure”, Journal of Financial and Quantitative Analysis, 40, 1-24.

*Leland, H. E. (1994), “Corporate Debt Value, Bond Covenants, and Optimal Capital Structure”, Journal of Finance, 49, 1213-1252.

*Leland, H. (1998), “Agency Costs, Risk Management, and Capital Structure”, Journal of Finance, 53, 1213-1243.

*Leland, H. E., and K. B. Toft (1996), “Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads”, Journal of Finance, 51, 987-1019.

*Longstaff, F. A., and E. S. Schwartz (1995), “A Simple Approach to Valuing Fixed and Floating Rate Debt”, Journal of Finance, 50, 789-819.

Merton, R. C. (1974), “On the Pricing of Corporate Debt: the Risk Structure of Interest Rates”, Journal of Finance, 29, 449-470.

*Sarkar, S., and F. Zapatero, 2003, "The Trade-Off Model with Mean-Reverting Earnings: Theory and Empirical Tests", The Economic Journal, 115, 834-860.

*Toft, K. B., and B. Prucyk (1997), “Options on Leveraged Equity: Theory and Empirical Tests”, Journal of Finance, 52, 1151-1180.

9. Exam

10. Project presentations.

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