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
Project presentation
Exam
Project
20%
10%
30%
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 nonexclusive.
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, 19812006.
*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, 377402.
*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, 71115.
*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.