Lower and Upper Pricing of Financial Assets

26 Pages Posted: 3 Dec 2020

See all articles by Robert J. Elliott

Robert J. Elliott

University of Calgary - Haskayne School of Business; University of Alberta - Department of Mathematical and Statistical Sciences; University of South Australia

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Ken Siu

Macquarie University; Financial Research Network (FIRN); Macquarie University, Macquarie Business School

Date Written: October 20, 2020

Abstract

Modeling of uncertainty by probability errs by ignoring the uncertainty in probability. When financial valuation recognizes the uncertainty of probability the best the market may offer is a two price framework of a lower and upper valuation. The martingale theory of asset prices is then replaced by the theory of nonlinear martingales. When dealing with pure jump compensators describing probability the uncertainty in probability is captured by introducing parametric measure distortions. The two price framework then alters asset pricing theory by requiring two required return equations one each for the lower upper valuation. Proxying lower and upper valuations by daily lows and highs the paper delivers the first empirical study of nonlinear martingales via the modeling and simultaneous estimation of the two required return equations.

Keywords: Bilateral Gamma Model, Acceptable Risks, Probability Distortions, Hidden Markov Model, Filtered Markets.

JEL Classification: G10, G12, G13

Suggested Citation

Elliott, Robert James and Madan, Dilip B. and Siu, Ken, Lower and Upper Pricing of Financial Assets (October 20, 2020). Available at SSRN: https://ssrn.com/abstract=3715608 or http://dx.doi.org/10.2139/ssrn.3715608

Robert James Elliott

University of Calgary - Haskayne School of Business ( email )

2500 University Drive, NW
Calgary, Alberta T2N 1N4
Canada

University of Alberta - Department of Mathematical and Statistical Sciences ( email )

Edmonton, Alberta T6G 2G1
Canada
403-492-5811 (Phone)
403-492-6826 (Fax)

University of South Australia ( email )

37-44 North Terrace
Adelaide
Australia

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

Ken Siu

Macquarie University ( email )

North Ryde
Sydney, New South Wales 2109
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

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