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Market Risk and Volatility in the Brazilian Stock Market

We estimate in this paper the market risk implied by the prices of different options traded in the Brazilian stock market. The fundamental theory to handle this problem is the one implied by the Arrow-Debreu contingent claim concept. Using that theory, we are able to construct the term structure of market risk, and to obtain a surface that provides slices for a particular “volatility smile.” The methodology that we use follows the one proposed by Shimko (1993), which is able to calculate a non-lognormal probability density function (PDF) consistent with the volatility observed in a relatively small sample of option prices. This methodology goes beyond the one proposed originally by Black and Scholes (1973), since it does not require log-normality of the PDF nor that volatility remains constant.

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Article provided by Universidad del CEMA in its journal Journal of Applied Economics.

Volume (Year): VI (2003)
Issue (Month): (November)
Pages: 385-403

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Handle: RePEc:cem:jaecon:v:6:y:2003:n:2:p:385-403
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  1. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
  2. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
  3. Narayana R. Kocherlakota, 1995. "The equity premium: it's still a puzzle," Discussion Paper / Institute for Empirical Macroeconomics 102, Federal Reserve Bank of Minneapolis.
  4. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  5. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  6. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
  7. Frank Milne & Dilip Madan, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Working Papers 1158, Queen's University, Department of Economics.
  8. Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
  9. Dilip B. Madan & Frank Milne, 1992. "Contingent Claims Valued and Hedged by Pricing and Investment in a Basis," Working Papers 868, Queen's University, Department of Economics.
  10. 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.
  11. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
  12. 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.
  13. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc.
  14. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
  15. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  16. 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.
  17. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  18. 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.
  19. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-72, October.
  20. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
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