Algebra of Stochastic Discount Factors — The Structural Theory of Asset Pricing (Part II)

The Capital Asset Pricing Model arises in an economy where agents have exponential utility functions and aggregate consumption is normally distributed, and gives the prices of assets with payoffs which are jointly normal with consumption. Such assets have normal marginal distributions and have dependence with consumption characterised by a normal copula. Wang has derived a transform which extends the CAPM by allowing pricing of assets in such an economy which have non-normal marginal distributions but still are normal-copula with consumption.Here we set out the stochastic discount factors corresponding to this version of the CAPM and to Wang’s transform, and show how to calculate stochastic discount factors and hence asset prices for assets whose dependence with consumption is non-normal. We show that the impact of dependency structure on asset prices is significant.

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Asset Pricing with Observable Stochastic Discount Factors

Journal of Economic Surveys ◽

10.1111/1467-6419.00173 ◽

2002 ◽

Vol 16 (3) ◽

pp. 397-446 ◽

Cited By ~ 37

Author(s):

Peter Smith ◽

Michael Wickens

Keyword(s):

Asset Pricing ◽

Discount Factors ◽

Stochastic Discount Factors

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Extension of the Capital Asset Pricing Model to Non-normal Dependence Structures

Astin Bulletin ◽

10.2143/ast.37.1.2020797 ◽

2007 ◽

Vol 37 (01) ◽

pp. 35-52 ◽

Cited By ~ 2

Author(s):

Mark Johnston

Keyword(s):

Asset Pricing ◽

Asset Prices ◽

Capital Asset Pricing ◽

Pricing Model ◽

Capital Asset ◽

Marginal Distributions ◽

Asset Pricing Model ◽

Discount Factors ◽

Stochastic Discount Factors ◽

Normal Copula

The Capital Asset Pricing Model arises in an economy where agents have exponential utility functions and aggregate consumption is normally distributed, and gives the prices of assets with payoffs which are jointly normal with consumption. Such assets have normal marginal distributions and have dependence with consumption characterised by a normal copula. Wang has derived a transform which extends the CAPM by allowing pricing of assets in such an economy which have non-normal marginal distributions but still are normal-copula with consumption.Here we set out the stochastic discount factors corresponding to this version of the CAPM and to Wang’s transform, and show how to calculate stochastic discount factors and hence asset prices for assets whose dependence with consumption is non-normal. We show that the impact of dependency structure on asset prices is significant.

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Asset Pricing and Portfolio Choice Theory

10.1093/acprof:oso/9780190241148.001.0001 ◽

2017 ◽

Cited By ~ 43

Author(s):

Kerry E. Back

Keyword(s):

Asset Pricing ◽

Portfolio Choice ◽

Continuous Time ◽

Choice Theory ◽

Discount Factors ◽

Long Run ◽

Asset Pricing Theory ◽

Stochastic Discount Factors ◽

Pricing Theory ◽

Continuous Time Models

This book is intended as a textbook for asset pricing theory courses at the Ph.D. or Masters in Quantitative Finance level and as a reference for financial researchers. The first two parts of the book explain portfolio choice and asset pricing theory in single‐period, discrete‐time, and continuous‐time models. For valuation, the focus throughout is on stochastic discount factors and their properties. Traditional factor models, including the CAPM, are related to or derived from stochastic discount factors. A chapter on stochastic calculus provides the needed tools for analyzing continuous‐time models. A chapter on “ex‐plaining puzzles” and the last two parts of the book provide introductions to a number of current topics in asset pricing research, including rare disasters, long‐run risks, external and internal habits, real options, corporate financing options, asymmetric and incomplete information, heterogeneous beliefs, and non‐expected‐utility preferences. Each chapter includes a “Notes and References” section and exercises for students.

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