IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Risk Aversion, Intertemporal Substitution, and Option Pricing

  • René Garcia

    (Crest)

  • Eric Renault

    (Crest)

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option pricing formula allows us to derive interesting characterizations of the volatility smile, that is the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words whenever the option pri

(This abstract was borrowed from another version of this item.)

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.crest.fr/content/blogcategory/21/54/
File Function: Crest working paper version
Download Restriction: no

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 98-10.

as
in new window

Length:
Date of creation: 1998
Date of revision:
Handle: RePEc:crs:wpaper:98-10
Contact details of provider: Postal: 15 Boulevard Gabriel Peri 92245 Malakoff Cedex
Phone: 01 41 17 60 81
Web page: http://www.crest.fr

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237.
  2. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Cecchetti, Stephen G. & Lam, Pok-sang & Mark, Nelson C., 1993. "The equity premium and the risk-free rate : Matching the moments," Journal of Monetary Economics, Elsevier, vol. 31(1), pages 21-45, February.
  4. René Garcia & Ramazan Gençay, 1998. "Pricing and Hedging Derivative Securities with Neural Networks and a Homogeneity Hint," CIRANO Working Papers 98s-35, CIRANO.
  5. René Garcia, 1995. "Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models," CIRANO Working Papers 95s-07, CIRANO.
  6. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, vol. 80(3), pages 398-418, June.
  7. Bailey, Warren & Stulz, René M., 1989. "The Pricing of Stock Index Options in a General Equilibrium Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(01), pages 1-12, March.
  8. Florens, J P & Mouchart, M, 1982. "A Note on Noncausality," Econometrica, Econometric Society, vol. 50(3), pages 583-91, May.
  9. repec:cup:cbooks:9780521589826 is not listed on IDEAS
  10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  11. Amin, Kaushik I & Ng, Victor K, 1993. " Option Valuation with Systematic Stochastic Volatility," Journal of Finance, American Finance Association, vol. 48(3), pages 881-910, July.
  12. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  13. Bossaerts, P.L.M. & Hillion, P., 1995. "Local Parametric Analysis of Hedging in Discrete Time," Discussion Paper 1995-23, Tilburg University, Center for Economic Research.
  14. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
  15. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1996. "Implied Volatility Functions: Empirical Tests," NBER Working Papers 5500, National Bureau of Economic Research, Inc.
  16. Dumas, Bernard J & Fleming, Jeff & Whaley, Robert E, 1996. "Implied Volatility Functions: Empirical Tests," CEPR Discussion Papers 1369, C.E.P.R. Discussion Papers.
  17. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
  18. Turnbull, Stuart M & Milne, Frank, 1991. "A Simple Approach to Interest-Rate Option Pricing," Review of Financial Studies, Society for Financial Studies, vol. 4(1), pages 87-120.
  19. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-36.
  20. repec:fth:inseep:9329 is not listed on IDEAS
  21. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-68, December.
  22. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  23. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
  24. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
  25. Marco Bonomo & René Garcia, 1994. "Disappointment Aversion as a Solution to the Equity Premium and the Risk-Free Rate Puzzles," CIRANO Working Papers 94s-14, CIRANO.
  26. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302.
  27. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. " General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
  28. Hansen, Lars Peter & Singleton, Kenneth J, 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 249-65, April.
  29. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  30. Christopher A. Sims, 1980. "Martingale-Like Behavior of Prices," NBER Working Papers 0489, National Bureau of Economic Research, Inc.
  31. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04.
  32. Marco antonio Bonomo & Rene Garcia, 1992. "Consumption and equilibrium asset pricing: An empirical assessment," Textos para discussão 284, Department of Economics PUC-Rio (Brazil).
  33. Florens, Jean-Pierre & Fougere, Denis, 1996. "Noncausality in Continuous Time," Econometrica, Econometric Society, vol. 64(5), pages 1195-1212, September.
  34. repec:cup:cbooks:9780521589819 is not listed on IDEAS
  35. repec:dgr:kubcen:199523 is not listed on IDEAS
  36. Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, . "General Properties of Option Prices (Revision of 11-95) (Reprint 058)," Rodney L. White Center for Financial Research Working Papers 1-96, Wharton School Rodney L. White Center for Financial Research.
  37. Aït-Sahalia, Yacine. & Bickel, Peter J. & Stoker, Thomas M., 1994. "Goodness-of-fit tests for regression using kernel methods," Working papers 3747-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  38. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  39. René Garcia & Éric Renault, 1997. "A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models," CIRANO Working Papers 97s-13, CIRANO.
  40. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
  41. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  42. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
  43. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1981. "A Re-examination of Traditional Hypotheses about the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 36(4), pages 769-99, September.
  44. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  45. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  46. Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-28, June.
  47. Gouriéroux, Christian & Monfort, Alain & Tenreiro, Carlos, 1994. "Kernel m-estimators : non parametric diagnostics for structural models," CEPREMAP Working Papers (Couverture Orange) 9405, CEPREMAP.
  48. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  49. repec:cup:cbooks:9780521589833 is not listed on IDEAS
  50. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:98-10. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Florian Sallaberry)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.