Sign Tests for Dependent Observations and Bounds for Path-Dependent Options
The present paper introduces new sign tests for testing for conditionally symmetric martingale-difference assumptions as well as for testing that conditional distributions of two (arbitrary) martingale-difference sequences are the same. Our analysis is based on the results that demonstrate that randomization over zero values of three-valued random variables in a conditionally symmetric martingale-difference sequence produces a stream of i.i.d. symmetric Bernoulli random variables and thus reduces the problem of estimating the critical values of the tests to computing the quantiles or moments of Binomial or normal distributions. The same is the case for randomization over ties in sign tests for equality of conditional distributions of two martingale-difference sequences. The paper also provides sharp bounds on the expected payoffs and fair prices of European call options and a wide range of path-dependent contingent claims in the trinomial financial market model in which, as is well-known, calculation of derivative prices on the base of no-arbitrage arguments is impossible. These applications show, in particular, that the expected payoff of a European call option in the trinomial model with log-returns forming a martingale-difference sequence is bounded from above by the expected payoff of a call option written on a stock with i.i.d. symmetric two-valued log-returns and, thus, reduce the problem of derivative pricing in the trinomial model with dependence to the i.i.d. binomial case. Furthermore, we show that the expected payoff of a European call option in the multiperiod trinomial option pricing model is dominated by the expected payoff of a call option in the two-period model with a log-normal asset price. These results thus allow one to reduce the problem of pricing options in the trinomial model to the case of two periods and the standard assumption of normal log-returns. We also obtain bounds on the possible fair prices of call options in the (incomplete) trinomial model in terms of the parameters of the asset's distribution. Sharp bounds completely similar to those for European call options also hold for many other contingent claims in the trinomial option pricing model, including those with an arbitrary convex increasing function as well as path-dependent ones, in particular, Asian options written on averages of the underlying asset's prices.
|Date of creation:||01 Jun 2005|
|Date of revision:||01 Jul 2005|
|Contact details of provider:|| Web page: http://icf.som.yale.edu/|
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- Jansen, Dennis W & de Vries, Casper G, 1991.
"On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective,"
The Review of Economics and Statistics,
MIT Press, vol. 73(1), pages 18-24, February.
- Dennis W. Jansen & Casper de Vries, 1988. "On the frequency of large stock returns: putting booms and busts into perspective," Working Papers 1989-006, Federal Reserve Bank of St. Louis.
- Breitung, Jörg & Gouriéroux, Christian, 1996.
"Rank tests for unit roots,"
SFB 373 Discussion Papers
1996,9, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Lo, Andrew W., 1987. "Semi-parametric upper bounds for option prices and expected payoffs," Journal of Financial Economics, Elsevier, vol. 19(2), pages 373-387, December.
- Tan, Baris & Yilmaz, Kamil, 2002.
"Markov chain test for time dependence and homogeneity: An analytical and empirical evaluation,"
European Journal of Operational Research,
Elsevier, vol. 137(3), pages 524-543, March.
- Tan, B. & Yilmaz, K., 1999. "Markov Chain Test for Time Dependence and Homogeneity: An Analytical and Empirical Evaluation," Papers 99/03, Koc University.
- Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-37, July.
- Bardia Kamrad & Peter Ritchken, 1991. "Multinomial Approximating Models for Options with k State Variables," Management Science, INFORMS, vol. 37(12), pages 1640-1652, December.
- Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
- Grundy, R.D., 1991. "Option Prices and the Underlying Asset's Return Distribution," Weiss Center Working Papers 11-91, Wharton School - Weiss Center for International Financial Research.
- Dufour, J.M. & Hallin, M., 1992.
"Improved Eaton Bounds for Linear Combinations of Bounded Random Variables with Statistical Applications,"
Cahiers de recherche
9224, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Dufour, J.M. & Hallin, M., 1992. "Improved Eaton Bounds for Linear Combinations of Bounded Random Variables with Statistical Applications," Cahiers de recherche 9224, Universite de Montreal, Departement de sciences economiques.
- Dufour, J-M. & Hallin, M., 1990. "Improved Eaton Bounds for Linear Combinations of Bounded Random Variables , with Statistical Applications," Papers 9104, Universite Libre de Bruxelles - C.E.M.E..
- Marc Hallin & Jean-Marie Dufour, 1993. "Improved Eaton bounds for linear combinations of bounded random variables, with statistical applications," ULB Institutional Repository 2013/2043, ULB -- Universite Libre de Bruxelles.
- Simon, S. & Goovaerts, M. J. & Dhaene, J., 2000. "An easy computable upper bound for the price of an arithmetic Asian option," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 175-183, May.
- Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March.
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- Ricardo J. Rodriguez, 2003. "Option Pricing Bounds: Synthesis And Extension," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 26(2), pages 149-164.
- McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
- Dufour, J.M. & Campbell, B., 1993.
"Exact Nonparametric Orthogonality and Random Walk Tests,"
Cahiers de recherche
9326, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Campbell, Bryan & Dufour, Jean-Marie, 1995. "Exact Nonparametric Orthogonality and Random Walk Tests," The Review of Economics and Statistics, MIT Press, vol. 77(1), pages 1-16, February.
- Perrakis, Stylianos, 1986. "Option Bounds in Discrete Time: Extensions and the Pricing of the American Put," The Journal of Business, University of Chicago Press, vol. 59(1), pages 119-41, January.
- Dahl, Christian M. & Nielsen, Steen, 2001. "The Random Walk Of Stock Prices: Implications Of Recent Nonpara-Metric Tests," Working Papers 07-2001, Copenhagen Business School, Department of Economics.
- Sharakhmetov, Sh. & Ibragimov, R., 2002. "A Characterization of Joint Distribution of Two-Valued Random Variables and Its Applications," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 389-408, November.
- Perrakis, Stylianos & Ryan, Peter J, 1984. " Option Pricing Bounds in Discrete Time," Journal of Finance, American Finance Association, vol. 39(2), pages 519-25, June.
- Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
- Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
- Bruce D. Grundy, . "Option Prices and the Underlying Asset's Return Distribution (Reprint 012)," Rodney L. White Center for Financial Research Working Papers 11-91, Wharton School Rodney L. White Center for Financial Research.
- Grundy, Bruce D, 1991. " Option Prices and the Underlying Asset's Return Distribution," Journal of Finance, American Finance Association, vol. 46(3), pages 1045-69, July.
- Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
- Jagannathan, Ravi, 1984. "Call options and the risk of underlying securities," Journal of Financial Economics, Elsevier, vol. 13(3), pages 425-434, September.
- Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 97-116.
- Rustam Ibragimov, 2004. "Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions," Econometric Society 2004 Latin American Meetings 105, Econometric Society.
- Parkinson, Michael, 1977. "Option Pricing: The American Put," The Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January.
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