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Taming the Skew: Higher-Order Moments in Modeling Asset Price Processes in Finance

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  • Sanjiv Ranjan Das
  • Rangarajan K. Sundaram

Abstract

It is widely acknowledged that many financial markets exhibit a considerably greater degree of kurtosis (and sometimes also skewness) than is consistent with the Geometric Brownian Motion model of Black and Scholes (1973). Among the many alternative models that have been proposed in this context, two have become especially popular in recent years: models of jump-diffusions, and models of stochastic volatility. This paper explores the statistical properties of these models with a view to identifying simple criteria for judging the consistency of either model with data from a given market; our specific focus is on the patterns of skewness and kurtosis that arise in each case as the length of the interval of observations changes. We find that, regardless of the precise parameterization employed, these patterns are strikingly similar within each class of models, enabling a simple consistency test along the desired lines. As an added bonus, we find that for most parameterizations, the set of possible patterns differs sharply across the two models, so that data from a given market will typically not be consistent with both models. However, there exist exceptional parameter configurations under which skewness and kurtosis in the two models exhibit remarkably similar behavior from a qualitative standpoint. The results herein will be useful to empiricists, theorists and practitioners looking for parsimonious models of asset prices.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5976.

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Date of creation: Mar 1997
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Handle: RePEc:nbr:nberwo:5976

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  1. 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.
  2. Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-63, December.
  3. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  4. 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.
  5. 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.
  6. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
  7. Chang Mo Ahn, 1992. "Option Pricing When Jump Risk Is Systematic," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 299-308.
  8. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
  9. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
  10. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  11. Ball, Clifford A & Torous, Walter N, 1985. " On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-73, March.
  12. Bodurtha, James N. & Courtadon, Georges R., 1987. "Tests of an American Option Pricing Model on the Foreign Currency Options Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(02), pages 153-167, June.
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Cited by:
  1. Maheu, John M. & McCurdy, Thomas H. & Zhao, Xiaofei, 2013. "Do jumps contribute to the dynamics of the equity premium?," Journal of Financial Economics, Elsevier, vol. 110(2), pages 457-477.
  2. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA.
  3. John M. Maheu & Thomas H. McCurdy, 2004. "News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns," Journal of Finance, American Finance Association, vol. 59(2), pages 755-793, 04.

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