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Projection Pricing

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  • D. G. Luenberger

Abstract

A significant problem in modern finance theory is how to price assets whose payoffs are outside the span of marketed assets. In practice, prices of assets are often assigned by using the capital asset pricing model (CAPM). If the market portfolio is efficient, the price obtained this way is equal to the price of an asset whose payoff, viewed as a vector in a Hilbert space of random variables, is projected orthogonally onto the space of marketed assets. This paper looks at the pricing problem from this projection viewpoint. It is shown that the results of the CAPM formula are duplicated by a formula based on the minimum-norm portfolio, and this pricing formula is valid even in cases when there is no efficient portfolio of risky assets. The relation of the pricing to other aspects of projection are also developed. In particular, a new pricing formula, called the correlation pricing formula, is developed that yields the same price as the CAPM, but is likely to be more accurate and more convenient than the CAPM in some cases.

Suggested Citation

  • D. G. Luenberger, 2001. "Projection Pricing," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 1-25, April.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:1:d:10.1023_a:1017596419383
    DOI: 10.1023/A:1017596419383
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    References listed on IDEAS

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    1. James E. Smith & Robert F. Nau, 1995. "Valuing Risky Projects: Option Pricing Theory and Decision Analysis," Management Science, INFORMS, vol. 41(5), pages 795-816, May.
    2. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    3. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
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    Cited by:

    1. David G. Luenberger, 2012. "Pricing dynamic binary variables and their derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 12(3), pages 451-464, April.

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