Jackwerth, Jens Carsten (1999): Option Implied RiskNeutral Distributions and Implied Binomial Trees: A Literature Review. Published in: Journal of Derivatives , Vol. 7, No. 2 (1999): pp. 6682.

PDF
MPRA_paper_11634.pdf Download (118kB)  Preview 
Abstract
In this selective literature review, we start by observing that in efficient markets, there is information incorporated in option prices that might help us to design option pricing models. To this end, we review the numerous methods of recovering riskneutral probability distributions from option prices at one particular time to expiration and their applications. Next, we move beyond one time to expiration to the construction of implied binomial trees, which model the stochastic process of the underlying asset. Finally, we describe extensions of implied binomial trees, and other nonparametric methods.
Item Type:  MPRA Paper 

Original Title:  Option Implied RiskNeutral Distributions and Implied Binomial Trees: A Literature Review 
English Title:  Option Implied RiskNeutral Distributions and Implied Binomial Trees: A Literature Review 
Language:  English 
Keywords:  Binomial Trees; RiskNeutral 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty G  Financial Economics > G3  Corporate Finance and Governance > G32  Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill 
Item ID:  11634 
Depositing User:  Jens Jackwerth 
Date Deposited:  20 Nov 2008 01:21 
Last Modified:  28 Sep 2019 09:56 
References:  Abadir, K., and M. Rockinger. “DensityEmbedding Functions.” Working paper, HEC, 1997. Abken, P., D. Madan, and S. Ramamurtie. “Estimation of RiskNeutral and Statistical Densities by Hermite Polynomial Approximation: With an Application to Eurodollar Futures Options.” Working paper, Federal Reserve Bank of Atlanta, 1996a. ——. “Pricing S&P 500 Index Options Using a Hilbert Space Basis.” Working paper, Federal Reserve Bank of Atlanta, 1996b. AitSahalia, Y., and A. Lo. “Nonparametric Estimation of StatePrice Densities Implicit in Financial Asset Prices.” Journal of Finance, 53, No. 2 (1998a), pp. 499547. ——. “Nonparametric Risk Management and Implied Risk Aversion.” Working paper, University of Chicago, 1998b. Andersen, L. “The Equity Option Volatility Smile: An Implicit Finite Difference Approach.” Working paper, General Re Financial Products Corp., 1995. Aparicio, S., and S. Hodges. “Implied RiskNeutral Distribution: A Comparison of Estimation Methods.” Working paper, Warwick University, 1998. Avellaneda, M., C. Friedman, R. Holmes, and D. Samperi. “Calibrating Volatility Surfaces Via RelativeEntropy Minimization.” Working paper, Courant Institute, New York University, 1996. Bahra, B. “Implied RiskNeutral Probability Density Functions from Option Prices: Theory and Application.” Working paper, Bank of England, 1997. Bakshi, G., C. Cao, and Z. Chen. “Empirical Performance of Alternative Option Pricing Models.” Journal of Finance, 52, No. 5 (1997), pp. 20032049. Banz, R., and M. Miller. “Prices for StateContingent Claims: Some Estimates and Applications.” Journal of Business, 51 (1978), pp. 653672. Barle, S., and N. Cakici. “How to Grow a Smiling Tree.” Journal of Financial Engineering, 7, No. 2 (1998), pp. 127146. Bates, D. “The Crash of ’87: Was it Expected? The Evidence from Options Markets.” Journal of Finance, 46, No. 3 (1991), pp. 10091044. ——. “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options.” Review of Financial Studies, 9, No. 1 (1996a), pp. 69107. ——. “Post’87 Crash Fears in S&P 500 Futures Options.” Journal of Econometrics, 1998. ——. “Testing Option Pricing Models.” In G. Maddala and C. Rao, eds., Handbook of Statistics, v. 14: Statistical Methods in Finance. Amsterdam: Elsevier, 1996b, pp. 567611. Bernardo, A., and O. Ledoit. “Gain, Loss and Asset Pricing.” Journal of Political Economy, forthcoming, 1999. Black, F., and M. Scholes. “Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), pp. 637659. Bodurtha, J., and M. Jermakyan. “NonParametric Estimation of an Implied Volatility Surface.” Working paper, Georgetown University, 1996a. ——. “Regular Smiles.” Working paper, Georgetown University, 1996b. Bookstaber, R., and J. McDonald. “A General Distribution for Describing Security Price Returns.” Journal of Business, 60, No. 3 (1987), pp. 401424. Bouchouev, I., and V. Isakov. “The Inverse Problem of Option Pricing.” Inverse Problems, 13 (1997), pp. L11L13. Breeden, D., and R. Litzenberger. “Prices of StateContingent Claims Implicit in Options Prices.” Journal of Business, 51 (1978), pp. 621651. Brenner, M., and Y. Eom. “NoArbitrage Option Pricing: New Evidence on the Validity of the Martingale Property.” Working paper, New York University, 1997. Brenner, M., Y. Eom, and Y. Landskroner. “Implied Foreign Exchange Rates Using Options Prices.” International Review of Financial Analysis, 5, No. 3 (1996), pp. 171183. BrittenJones, M., and A. Neuberger. “Option Prices, Implied Price Processes, and Stochastic Volatility.” Journal of Finance, forthcoming, 1999. Brown, G., and K.B. Toft. “Constructing Binomial Trees from Multiple Implied Probability Distributions.” Journal of Derivatives, 7, No. 2 (1999). Buchen, P., and M. Kelly. “The Maximum Entropy Distribution of an Asset Inferred from Option Prices.” Journal of Financial and Quantitative Analysis, 31, No. 1 (1996), pp. 143159. Campa, J., and K. Chang. “Arbitrage Based Tests of Target Zone Credibility: Evidence from ERM CrossRate Options.” American Economic Review, 86 (1996), pp. 726740. ——. “ERM Realignment Risk and its Economic Determinants as Reflected in CrossRate Options.” Economic Journal, 108, No. 449 (1998), pp. 10461066. Campa, J., K. Chang, and J. Refalo. “An OptionsBased Analysis of Emerging Market Exchange Rate Expectations: Brazil’s Real Plan, 19941999.” Working paper, New York University, 1999. Campa, J., K. Chang, and R. Reider. “Implied Exchange Rate Distributions: Evidence from OTC Option Markets.” Journal of International Money and Finance, 17, No. 1 (1998), pp. 117160. Carr, P., and D. Madan. “Determining Volatility Surfaces and Option Values from an Implied Volatility Smile.” Working paper, University of Maryland, 1998. Chriss, N. “Transatlantic Trees.” Risk, 9 (1996), pp. 4548. Cochrane, J., and J. SaaRequejo. “Beyond Arbitrage: Good Deal Asset Price Bounds in Incomplete Markets.” Journal of Political Economy, forthcoming, 1999. Coleman, T., Y. Li, and A. Verma. “Reconstructing the Unknown Volatility Function.” Working paper, Cornell University, 1998. Cont, R. “Beyond Implied Volatility.” In J. Kertesz and I. Kondor, eds., Econophysics. Dordrecht: Kluwer, 1997. Corrado, C., and T. Su. “Implied Volatility Skews and Stock Index Skewness and Kurtosis Implied by S&P 500 Index Option Prices.” Journal of Derivatives, 4, No. 4 (1997), pp. 819. ——. “Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices.” Journal of Financial Research, 19, No. 2 (1996), pp. 175192. Coutant, S., E. Jondeau, and M. Rockinger. “Reading Interest Rate and Bond Futures Options’ Smiles: How PIBOR and Notional Operators Appreciated the 1997 French Snap Election.” Working paper, HEC, 1998. Cox, J., S. Ross, and M. Rubinstein. “Option Pricing: A Simplified Approach.” Journal of Financial Economics, 7, No. 3 (1979), pp. 229263. Derman, E., and I. Kani. “Riding on a Smile.” Risk, 7, No. 2 (1994), pp. 3239. ——. “Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility.” International Journal of Theoretical and Applied Finance, 1 (1998), pp. 722. Derman, E., I. Kani, and N. Chriss. “Implied Trinomial Trees of the Volatility Smile.” Journal of Derivatives, 3, No. 4 (1996), pp. 722. Dumas, B., J. Fleming, and R. Whaley. “Implied Volatility Functions: Empirical Tests.” Journal of Finance, 53, No. 6 (1998), pp. 20592106. Dupire, B. “Pricing With a Smile.” Risk, 7, No. 1 (1994), pp. 1820. Hartvig, N., J. Jensen, and J. Pedersen. “Risk Neutral Densities of the ‘Christmas Tree’ Type.” Working paper, Centre for Mathematical Physics and Stochastics, Aarhus University, 1999. Heath, D., R. Jarrow, and A. Morton. “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation.” Econometrica, 60, No. 1 (1992), pp. 77105. Herrmann, R., and A. Narr. “Risk Neutrality.” Risk, 10 (1997), Technology Supplement, pp. 2329. Hutchinson, J., A. Lo, and T. Poggio. “A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks.” Journal of Finance, 49, No. 3 (1994), pp. 851889. Jackwerth, J. “Generalized Binomial Trees.” Journal of Derivatives, 5, No. 2 (1997), pp. 717. ——. “Recovering Risk Aversion from Option Prices and Realized Returns.” Review of Financial Studies, forthcoming, 1999. Jackwerth, J., and M. Rubinstein. “Recovering Probability Distributions from Option Prices.” Journal of Finance, 51 (1996), pp. 16111631. ——. “Recovering Stochastic Processes from Option Prices.” Working paper, University of Wisconsin, Madison, 1998. Jarrow, R., and A. Rudd. “Approximate Valuation for Arbitrary Stochastic Processes.” Journal of Financial Economics, 10, No. 3 (1982), pp. 347369. Johnson, N. “Systems of Frequency Curves Generated by Methods of Translation.” Biometrika, 36 (1949), pp. 149176. Jondeau, E., and M. Rockinger. “Estimating GramCharlier Expansions under Positivity Constraints.” Working paper, HEC, 1998a. ——. “Reading the Smile: The Message Conveyed by Methods Which Infer Risk Neutral Densities.” Working paper, HEC, 1998b. Lagnado, R., and S. Osher. “Reconciling Differences.” Risk, 10, No. 4 (1997), pp. 7983. Laurent, J., and D. Leisen. “Building a Consistent Pricing Model from Observed Option Prices.” Working paper, Hoover Institute, Stanford University, 1998. Leahy, M., and C. Thomas. “The Sovereignty Option: The Quebec Referendum and Market Views on the Canadian Dollar.” Working paper, Federal Reserve Board, 1996. Ledoit, O., and P. SantaClara. “Relative Pricing of Options with Stochastic Volatility.” Working paper, UCLA, 1998. Longstaff, F. “Martingale Restriction Tests of Option Pricing Models.” Working paper, University of California, Los Angeles, 1990. ——. “Option Pricing and the Martingale Restriction.” Review of Financial Studies, 8, No. 4 (1995), pp. 10911124. Malz, A. “Estimating the Probability Distribution of the Future Exchange Rate from Option Prices.” Journal of Derivatives, 5, No. 2 (1997), pp. 1836. ——. “Using Option Prices to Estimate Realignment Probabilities in the European Monetary System: The Case of Sterling Mark.” Journal of International Money and Finance, 15, No. 5 (1996), pp. 717748. Masson, J., and S. Perrakis. “A Jumping Smile.” Working paper, University of Ottawa, 1997. Mayhew, S. “On Estimating the RiskNeutral Probability Distribution Implied by Option Prices.” Working paper, Purdue University, 1995. McCauley, R., and W. Melick. “Risk Reversal Risk.” Risk, 9, No. 11 (1996), pp. 5457. Melick, W., and C. Thomas. “Recovering an Asset’s Implied PDF from Option Prices: An Application to Crude Oil During the Gulf Crisis.” Journal of Financial and Quantitative Analysis, 32 (1997), pp. 91115. Mizrach, B. “Did Option Prices Predict the ERM Crisis?” Working paper, Rutgers University, 1996. Osborne, M. “Brownian Motion in the Stock Market.” Operations Research, 7 (1959), pp. 145173. Posner, S., and M. Milevsky. “Valuing Exotic Options by Approximating the SPD with Higher Moments.” Journal of Financial Engineering, 7, No. 2 (1998), pp. 109125. Potters, M., R. Cont, and J. Bouchaud. “Financial Markets as Adaptive Systems.” Europhysics Letters, 41, No. 3 (1998), pp. 239244. Pritsker, M. “Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models.” Working paper, Federal Reserve Board, Washington, DC, 1997. Ritchey, R. “Call Option Valuation for Discrete Normal Mixtures.” Journal of Financial Research, 13, No. 4 (1990), pp. 285295. Rookley, C. “Fully Exploiting the Information Content of Intra Day Option Quotes: Applications in Option Pricing and Risk Management.” Working paper, University of Arizona, 1997. Rosenberg, J. “Pricing Multivariate Contingent Claims Using Estimated RiskNeutral Density Functions.” Working paper, University of California, San Diego, 1996. Rosenberg, J., and R. Engle. “Option Hedging Using Empirical Pricing Kernels.” Working paper, New York University, 1997. Ross, S. “Options and Efficiency.” Quarterly Journal of Economics, 90 (1976), pp. 7589. Rubinstein, M. “Edgeworth Binomial Trees.” Journal of Derivatives, 5, No. 3 (1998), pp. 2027. ——. “Implied Binomial Trees.” Journal of Finance, 49, No. 3 (1994), pp. 771818. ——. “Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978.” Journal of Finance, 40, No. 2 (1985), pp. 455480. Samperi, D. “Implied Trees in Incomplete Markets.” Working paper, Courant Institute, New York University, 1996. Sherrick, B., P. Garcia, and V. Tirupattur. “Recovering Probabilistic Information from Option Markets: Tests of Distributional Assumptions.” Working paper, University of Illinois at UrbanaChampaign, 1995. Sherrick, B., S. Irwin, and D. Forster. “An Examination of OptionImplied S&P 500 Futures Price Distributions.” Financial Review, 31, No. 3 (1996), pp. 667694. ——. “OptionBased Evidence of the Nonstationarity of Expected S&P 500 Futures Price Distributions.” Journal of Futures Markets, 12, No. 3 (1992), pp. 275290. Shimko, D. “Bounds on Probability.” Risk, 6 (1993), pp. 3337. Söderlind, P., and L. Svensson. “New Techniques to Extract Market Expectations from Financial Instruments.” Working paper, Stockholm School of Economics, 1996. Stutzer, M. “A Simple Nonparametric Approach to Derivative Security Valuation.” Journal of Finance, 51 (1996), pp. 16331652. Toft, K., and B. Prucyk. “Options on Leveraged Equity: Theory and Empirical Tests.” Journal of Finance, 52, No. 3 (1997), pp. 11511180. Tompkins, R. “Implied Volatility Surfaces: Uncovering the Regularities for Options on Financial Futures.” Working paper, Vienna University of Technology and Warwick University, 1998. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/11634 