Annals of Finance

, Volume 15, Issue 1, pp 29–58 | Cite as

Conic asset pricing and the costs of price fluctuations

  • Dilip B. MadanEmail author
  • Wim Schoutens
Research Article


Prudent upper and lower valuations from the literature on arbitrage free two price economies provide risk characteristics driving required returns. The risk characteristics assess the risk of price fluctuations. The difference between the upper and lower prudent valuations can be viewed as a capital charge. In addition the lower valuation assesses the down side tail risk. The required risk characteristics may be estimated on a daily basis from past data and we elaborate on how to perform such upper and lower valuations using distorted expectations. Details are provided for calculations using just the raw data, or by first fitting a probability distribution, or in terms of estimated arrival rates for jumps. The valuations are obtained with a dynamic calibration of a parametric distortion on the S&P 500 index options market. Results for required returns based on capital charges and down side risk compensation show an improvement when risk is represented by the arrival rates of jump sizes. For risk assessments based on arrival rates, capital charges constitute between 67 and 85% of the required return. The rest being a charge for downside risk exposures. After the introduction of risk characteristics into required returns there is little scope for covariation measures like asset betas. Different proposed constructions for required returns deliver differences in the value of an invested dollar and associated differences in asset rankings across time.


Probability distortion Measure distortion Self decomposable law Variance gamma model 

JEL Classification

G10 G12 G13 


Compliance with ethical standards

Conflict of interest

Both the authors declare that there is no conflict of interest.


  1. Back, K.E.: Asset Pricing and Portfolio Choice Theory. Oxford: Oxford University Press (2010)Google Scholar
  2. Barndorff-Nielsen, O.E., Shiryaev, A.: Change of Time and Change of Measure. Singapore: World Scientific Press (2010)Google Scholar
  3. Bion-Nadal, J.: Bid-ask dynamic pricing in financial markets with transactions costs and liquidity risk. J Math Econ 45, 738–750 (2009)CrossRefGoogle Scholar
  4. Black, F.: Estimating expected return. Financ Anal J 49, 36–38 (1993)CrossRefGoogle Scholar
  5. Brennan, M.J., Chordia, T., Subrahmanyam, A.: Alternative factor specifications, security characteristics, and the cross-section of expected stock returns. J Financ Econ 49, 345–373 (1998)CrossRefGoogle Scholar
  6. Carr, P., Geman, H., Madan, D., Yor, M.: The fine structure of asset returns: an empirical investigation. J Bus 75, 305–332 (2002)CrossRefGoogle Scholar
  7. Carr, P., Geman, H., Madan, D.B., Yor, M.: Self-decomposability and option pricing. Math Finance 17, 31–57 (2007)CrossRefGoogle Scholar
  8. Carr, P., Madan, D.B., Vicente Alvarez, J.J.: Markets, profits, capital, leverage and returns. J Risk 14, 95–122 (2011)Google Scholar
  9. Cherny, A., Madan, D.B.: New measures for performance evaluation. Rev Financ Stud 22, 2571–2606 (2009)CrossRefGoogle Scholar
  10. Choquet, G.: Theory of capacities. Ann Inst Fourier 5, 131–295 (1953)CrossRefGoogle Scholar
  11. Chordia, T., Goyal, A., Shanken, J.: Cross-sectional asset pricing with individual stocks: betas versus characteristics. Working Paper, Emory University. (2015)
  12. Eberlein, E., Madan, D.B.: The Distribution of returns at longer horizons. In: Kijima, M., Hara, C., Muromachi, Y., Nakaoka, H., Nishide, K. (eds.) Recent Advances in Financial Engineering; Proceedings of the KIER-TMU Workshop. Singapore: World Scientific (2010)Google Scholar
  13. Eberlein, E., Madan, D., Pistorius, M., Yor, M.: Bid and ask prices as non-linear continuous time G-expectations based on distortions. Math Financ Econ 8, 265–289 (2014)CrossRefGoogle Scholar
  14. Fama, E.F., French, K.R.: The cross-section of expected stock returns. J Finance 47, 427–465 (1992)CrossRefGoogle Scholar
  15. Fama, E.F., French, K.R.: Common risk factors in the returns on stocks and bonds. J Financ Econ 33, 3–56 (1993)CrossRefGoogle Scholar
  16. Guasoni, P., Lepinette, E., Rasonyi, M.: The fundamental theorem of asset pricing under transactions costs. Finance Stoch 16, 741–777 (2012)CrossRefGoogle Scholar
  17. Jouini, E., Kallal, H.: Martingale and arbitrage in securities markets with transaction cost. J Econ Theory 66, 178–197 (1995)CrossRefGoogle Scholar
  18. Khintchine, A.Y.: Limit Laws of Sums of Independent Random Variables. Moscow: ONTI (1938) (Russian) Google Scholar
  19. Lévy, P.: Théorie de l’Addition des Variables Alé atoires. Paris: Gauthier-Villars (1937)Google Scholar
  20. Lintner, J.: The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat 47, 13–37 (1965)CrossRefGoogle Scholar
  21. Madan, D.B.: Estimating parametric models of probability distributions. Methodol Comput Appl Probab 17, 823–831 (2015a)CrossRefGoogle Scholar
  22. Madan, D.B.: Asset pricing theory for two price economies. Ann Finance 11, 1–35 (2015b)CrossRefGoogle Scholar
  23. Madan, D.B.: Efficient estimation of expected stock price returns. Finance Res Lett 23, 31–38 (2017)CrossRefGoogle Scholar
  24. Madan, D.B.: Instantaneous portfolio theory. Quant Finance (2018).
  25. Madan, D.B., Schoutens, W.: Applied Conic Finance. Cambridge: Cambridge University Press (2016)Google Scholar
  26. Madan, D., Seneta, E.: The variance gamma (VG) model for share market returns. J Bus 63, 511–524 (1990)CrossRefGoogle Scholar
  27. Madan, D., Carr, P., Chang, E.: The variance gamma process and option pricing. Rev Finance 2, 79–105 (1998)CrossRefGoogle Scholar
  28. Mossin, J.: Equilibrium in a capital asset market. Econometrica 35, 768–783 (1966)CrossRefGoogle Scholar
  29. Ross, S.A.: Arbitrage theory of capital asset pricing. J Econ Theory 13, 341–360 (1976)CrossRefGoogle Scholar
  30. Ross, S.: A simple approach to the valuation of risky streams. J Bus 51, 453–475 (1978)CrossRefGoogle Scholar
  31. Sato, K.: Self similar processes with independent increments. Probab Theory Relat Fields 89, 285–300 (1991)CrossRefGoogle Scholar
  32. Sato, K.: Lévy Processes and Infinitely Divisible Distributions. Cambridge: Cambridge University Press (1999)Google Scholar
  33. Sharpe, W.F.: Capital asset prices: a theory of market equilibrium under conditions of risk. J Finance 19, 425–442 (1964)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege ParkUSA
  2. 2.K. U. LeuvenLeuvenBelgium

Personalised recommendations