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Erschienen in:
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2019 | OriginalPaper | Buchkapitel

1. Stochastic Dominance: Introduction

verfasst von : Stylianos Perrakis

Erschienen in: Stochastic Dominance Option Pricing

Verlag: Springer International Publishing

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Abstract

Stochastic dominance is a concept about choice under risk that was originally derived from the economics literature for the ordering of uncertain prospects by a particular set of investors. This chapter reviews the early definitions and applications, which started in 1962 with a contribution in the economics literature by Quirk and Saposnik and expanded into mathematics, finance and possibly other fields as well. It focuses on the stochastic dominance results that have implications for the study of option markets, including valuable econometric tests of pairwise comparisons of time series.

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Nächstes Kapitel Stochastic Dominance Option Pricing I: The Frictionless Case
Fußnoten
1
The presentation of the dominance conditions (1.3a, 1.3b, 1.3c) follows the more general Hanoch and Levy (1969) that defines the domain of the distributions as the entire real line and covers all types of distributions. In practice all our useful results are restricted to the positive real line.
 
2
In fact, the classic analysis of risk in Rothschild and Stiglitz (1970) shows that risk comparisons between two distributions are not equivalent to comparisons of their variances.
 
3
These are presented in the survey article by Levy (1992).
 
4
Multiperiod SSD rules presented in Levy (2016, Chapter 13) are not practical for option market applications.
 
5
Another definition involving the risk premium necessary to subtract from the mean of the risky prospect to represent expected utility was shown to be equivalent to the others; see Levy (2016, Chapter 8).
 
6
See Levy (1977).
 
7
Except where otherwise specified, all information in this section is from the survey article by Levy (1992); see also Levy (2016, Chapters 9 and 11).
 
8
See Shalit and Yitzhaki (1994).
 
9
See, for instance, Grauer and Hakansson (1987).
 
10
See Kuosmanen (2004), Post (2003) and Scaillet and Topaloglou (2010).
 
11
See Anderson (1996), Davidson and Duclos (2000) and Barrett and Donald (2003).
 
12
See Constantinides et al. (2017).
 
Literatur
Anderson, G.J. 1996. Nonparametric Tests of Stochastic Dominance in Income Distributions. Econometrica 64: 1183–1193.CrossRef
Arrow, K.J. 1965. Aspects of the Theory of Risk Bearing. Helsinki: Yrjo Jahnssonin Saatio.
Barrett, G., and S. Donald. 2003. Consistent Tests for SD. Econometrica 71: 71–104.CrossRef
Constantinides, George M., Michal Czerwonko, Jens C. Jackwerth, and Stylianos Perrakis. 2011. Are Options on Index Futures Profitable for Risk Averse Investors? Empirical Evidence. Journal of Finance 66: 1407–1437.CrossRef
Constantinides, George M., Michal Czerwonko, and Stylianos Perrakis. 2017. Mispriced Option Portfolios. NBER Working Paper #23708.
Davidson, Russell. 2009. Testing for Restricted Stochastic Dominance: Some Further Results. Review of Economic Analysis 1: 34–59.
Davidson, Russell, and Jean-Yves Duclos. 2000. Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality. Econometrica 68: 1435–1464.CrossRef
———. 2013. Testing for Restricted Stochastic Dominance. Econometric Reviews 32: 84–125.CrossRef
Eeckhoudt, L., and H. Schlesinger. 2006. Putting Risk in Its Proper Place. American Economic Review 96: 280–289.CrossRef
Grauer, R., and Nils Hakansson. 1987. Gains from International Diversification: 1968–85 Returns on Portfolios of Stocks and Bonds. Journal of Finance 42: 721–739.CrossRef
Hadar, J., and W. Russell. 1969. Rules for Ordering Uncertain Prospects. American Economic Review 59: 25–34.
Hanoch, G., and H. Levy. 1969. The Efficiency Analysis of Choices Involving Risk. Review of Economic Studies 36: 335–346.CrossRef
Kroll, Y., H. Levy, and H. Markowitz. 1984. Mean-Variance Versus Direct Utility Maximization. Journal of Finance 39: 47–61.CrossRef
Kuosmanen, T. 2004. Efficient Diversification According to Stochastic Dominance Criteria. Management Science 50: 1390–1406.CrossRef
Levy, H. 1977. The Definition of Risk: An Extension. Journal of Economic Theory 14: 232–234.CrossRef
Levy, Haim. 1992. Stochastic Dominance and Expected Utility: Survey and Analysis. Management Science 38: 555–593.CrossRef
Levy, H., and Y. Kroll. 1978. Ordering Uncertain Options with Borrowing and Lending. Journal of Finance 33: 552–573.CrossRef
Markowitz, H.M. 1952. Portfolio Selection. Journal of Finance 7: 77–91.
Post, Thierry. 2003. Empirical Tests for Stochastic Dominance Efficiency. Journal of Finance 58: 1905–1932.CrossRef
Pratt, J.W. 1964. Risk Aversion in the Small and in the Large. Econometrica 32: 122–136.CrossRef
Quirk, J.P., and R. Saposnik. 1962. Admissibility and Measurable Utility Function. Review of Economic Studies 29: 140–146.CrossRef
Rothschild, M., and J.E. Stiglitz. 1970. Increasing Risk. I. A Definition. Journal of Economic Theory 2: 225–243.CrossRef
Scaillet, O., and N. Topaloglou. 2010. Testing for Stochastic Dominance Efficiency. Journal of Business and Economic Statistics 28: 169–180.CrossRef
Shalit, H., and S. Yitzhaki. 1994. Marginal Conditional Stochastic Dominance. Management Science 40: 670–684.CrossRef
Whitmore, G.A. 1970. Third Degree Stochastic Dominance. American Economic Review 60: 457–459.
Metadaten
Titel
Stochastic Dominance: Introduction
verfasst von
Stylianos Perrakis
Copyright-Jahr
2019
Buch
Stochastic Dominance Option Pricing

Print ISBN: 978-3-030-11589-0

Electronic ISBN: 978-3-030-11590-6

Copyright-Jahr: 2019

DOI
https://doi.org/10.1007/978-3-030-11590-6_1