Implied risk-neutral probability density functions from option prices: theory and application
Due to their forward-looking nature, derivative markets provide monetary authorities with a rich source of information for gauging market sentiment. For example, a futures price gives a widely used measure of the market's views about the future value of an asset, namely its mean or expected value at the maturity date of the futures contract. Moreover, the information available from futures prices can be extended by using option prices to estimate the market's entire probability distribution of the future value of an asset. This paper develops various techniques for estimating the market's probability distribution of the future value of an underlying asset from the prices of options on that asset. It discusses the relative merits and drawbacks of each approach, and shows how our preferred approach can be applied to estimate ex ante probability distributions using LIFFE equity and interest rate options, and Philadelphia Stock Exchange currency options. The paper then illustrates the potential value of this type of information to the policy-maker in assessing monetary conditions and conducting monetary operations. Finally, the paper looks at the limitations in data availability and highlights some areas for future research.
|Date of creation:||Jul 1997|
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- Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, Oxford University Press, vol. 90(1), pages 75-89.
- Neuhaus, Holger, 1995. "The information content of derivatives for monetary policy: Implied volatilities and probabilities," Discussion Paper Series 1: Economic Studies 1995,03e, Deutsche Bundesbank, Research Centre.
- Whaley, Robert E., 1982. "Valuation of American call options on dividend-paying stocks : Empirical tests," Journal of Financial Economics, Elsevier, vol. 10(1), pages 29-58, March.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
- 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.
- 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.
- King, Mervyn, 1995. "Credibility and Monetary Policy: Theory and Evidence," Scottish Journal of Political Economy, Scottish Economic Society, vol. 42(1), pages 1-19, February.
- K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," Review of Economic Studies, Oxford University Press, vol. 31(2), pages 91-96.
- MacBeth, James D & Merville, Larry J, 1980. " Tests of the Black-Scholes and Cox Call Option Valuation Models," Journal of Finance, American Finance Association, vol. 35(2), pages 285-301, May.
- Allan M. Malz, 1995. "Using option prices to estimate realignment probabilities in the European Monetary System," Staff Reports 5, Federal Reserve Bank of New York.
- Jens Carsten Jackwerth and Mark Rubinstein., 1995. "Implied Probability Distributions: Empirical Analysis," Research Program in Finance Working Papers RPF-250, University of California at Berkeley.
- 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.
- Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
- Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
- Ball, Clifford A. & Torous, Walter N., 1983. "A Simplified Jump Process for Common Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 53-65, March.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- Yacine Aït-Sahalia & Andrew W. Lo, .
"Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices,"
CRSP working papers
332, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
- 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.
- 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.
- Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-96, Winter.
- Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
- 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.
- 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.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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