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Options and volatility

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Author Info
Peter A. Abken
Saikat Nandi
Abstract

Because volatility of the underlying asset price is a critical factor affecting option prices and hedge ratios, the modeling of volatility and its dynamics is of vital interest to traders, investors, and risk managers. This modeling is a difficult task because the path of volatility during the life of an option is highly unpredictable. There has been a proliferation of volatility specifications since the original, simple constant-volatility assumption of the famous Black and Scholes option pricing model. This article gives an overview of different specifications of asset price volatility that are widely used in option pricing models. ; While the authors cite evidence that some stochastic-volatility option pricing models provide better market prices and hedges than the Black-Scholes model, they acknowledge that for both academic researchers and market practitioners, no consensus exists regarding the best specification of volatility for option pricing. Although a number of alternative approaches can account, at least partially, for the pricing deficiencies of the Black-Scholes models, none dominates as a clearly superior approach for pricing options.

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Publisher Info
Article provided by Federal Reserve Bank of Atlanta in its journal Economic Review.

Volume (Year): (1996)
Issue (Month): Dec ()
Pages: 21-35
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:fip:fedaer:y:1996:i:dec:p:21-35:n:v.81no3-6

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Related research
Keywords: Options (Finance);

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  1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 4(4), pages 727-52. [Downloadable!] (restricted)
  2. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-78, December. [Downloadable!] (restricted)
    Other versions:
  3. 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. [Downloadable!] (restricted)
  4. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311. [Downloadable!] (restricted)
  5. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," Journal of Business, University of Chicago Press, vol. 36, pages 394. [Downloadable!]
  6. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1996. "Implied Volatility Functions: Empirical Tests," NBER Working Papers 5500, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  7. Duffie, J Darrell & Huang, Chi-fu, 1985. "Implementing Arrow-Debreu Equilibria by Continuous Trading of Few Long-lived Securities," Econometrica, Econometric Society, vol. 53(6), pages 1337-56, November. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
    Other versions:
  10. Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April. [Downloadable!] (restricted)
  11. Peter A. Abken & Dilip B. Madan & Sailesh Ramamurtie, 1996. "Estimation of risk-neutral and statistical densities by Hermite polynomial approximation: with an application to Eurodollar futures options," Working Paper 96-5, Federal Reserve Bank of Atlanta. [Downloadable!]
  12. Peter A. Abken & Hugh Cohen, 1994. "Generalized method of moments estimation of Heath-Jarrow-Morton models of interest-rate contingent claims," Working Paper 94-8, Federal Reserve Bank of Atlanta.
  13. Angelo Melino & Stuart M. Turnbull, 1991. "The Pricing of Foreign Currency Options," Canadian Journal of Economics, Canadian Economics Association, vol. 24(2), pages 251-81, May. [Downloadable!] (restricted)
  14. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 293-326. [Downloadable!] (restricted)
  17. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December. [Downloadable!]
  18. Dumas, Bernard J & Fleming, Jeff & Whaley, Robert E, 1996. "Implied Volatility Functions: Empirical Tests," CEPR Discussion Papers 1369, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  19. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June. [Downloadable!] (restricted)
  20. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
  21. Back, Kerry, 1993. "Asymmetric Information and Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(3), pages 435-72. [Downloadable!] (restricted)
  22. Jaesun Noh & Robert F. Engle & Alex Kane, 1994. "Forecasting Volatility and Option Prices of the S&P 500 Index," University of California at San Diego, Economics Working Paper Series 93-32r, Department of Economics, UC San Diego. [Downloadable!]
  23. Peter A. Abken, 1994. "Over-the-counter financial derivatives: risky business?," Economic Review, Federal Reserve Bank of Atlanta, issue Mar, pages 1-22.
  24. Saikat Nandi, 1996. "Pricing and hedging index options under stochastic volatility: an empirical examination," Working Paper 96-9, Federal Reserve Bank of Atlanta. [Downloadable!]
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