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Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices

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  • Yacine Ait-Sahalia
  • Andrew W. Lo

Abstract

Implicit in the prices of traded financial assets are Arrow- Debreu state prices or, in the continuous-state case, the state-price density (SPD). We construct an estimator for the SPD implicit in option prices and derive an asymptotic sampling theory for this estimator to gauge its accuracy. The SPD estimator provides an arbitrage-free method of pricing new, more complex, or less liquid securities while capturing those features of the data that are most relevant from an asset-pricing perspective, e.g., negative skewness and excess kurtosis for asset returns, volatility 'smiles' for option prices. We perform Monte Carlo simulation experiments to show that the SPD estimator can be successfully extracted from option prices and we present an empirical application using S&P 500 index options.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5351.

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Date of creation: Nov 1995
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Handle: RePEc:nbr:nberwo:5351

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  1. 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.
  2. Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
  3. 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.
  4. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
  5. 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.
  6. 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.
  7. Constantinides, George M, 1982. "Intertemporal Asset Pricing with Heterogeneous Consumers and without Demand Aggregation," The Journal of Business, University of Chicago Press, vol. 55(2), pages 253-67, April.
  8. 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.
  9. Bick, Avi, 1990. " On Viable Diffusion Price Processes of the Market Portfolio," Journal of Finance, American Finance Association, vol. 45(2), pages 673-89, June.
  10. Chiras, Donald P. & Manaster, Steven, 1978. "The information content of option prices and a test of market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 213-234.
  11. Black, Fischer & Scholes, Myron S, 1972. "The Valuation of Option Contracts and a Test of Market Efficiency," Journal of Finance, American Finance Association, vol. 27(2), pages 399-417, May.
  12. Boyle, Phelim P. & Emanuel, David, 1980. "Discretely adjusted option hedges," Journal of Financial Economics, Elsevier, vol. 8(3), pages 259-282, September.
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