Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review

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 risk-neutral 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 non-parametric methods.

[1]  D. Heath,et al.  Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation , 1990, Journal of Financial and Quantitative Analysis.

[2]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[3]  S. Irwin,et al.  Option‐based evidence of the nonstationarity of expected S&P 500 futures price distributions , 1992 .

[4]  J. Rosenberg.  Pricing Multivariate Contingent Claims Using Estimated Risk-Neutral Density Functions , 1997 .

[5]  M. Stutzer.  A Simple Nonparametric Approach to Derivative Security Valuation , 1996 .

[6]  Allan M. Malz.  Using option prices to estimate realignment probabilities in the European Monetary System: the case of sterling-mark , 1996 .

[7]  R. J. Ritchey,et al.  CALL OPTION VALUATION FOR DISCRETE NORMAL MIXTURES , 1990 .

[8]  Jean-Paul Laurent,et al.  Building a Consistent Pricing Model from Observed Option Prices , 1998 .

[9]  Jeff Fleming,et al.  Implied volatility functions: empirical tests , 1996, IEEE/IAFE 1996 Conference on Computational Intelligence for Financial Engineering (CIFEr).

[10]  J. Jackwerth.  Recovering Risk Aversion from Option Prices and Realized Returns , 1998 .

[11]  M. Pritsker.  Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models , 1998 .

[12]  K. Toft.,et al.  Options on Leveraged Equity: Theory and Empirical Tests , 1997 .

[13]  James B. McDonald,et al.  A General Distribution for Describing Security Price Returns , 1987 .

[14]  Cameron Rookley.  Fully Exploiting the Information Content of Intra Day Option Quotes: Applications in Option Pricing , 1997 .

[15]  S. Irwin,et al.  An examination of option-implied s&p 500 futures price distributions , 1996 .

[16]  Bhupinder Bahra.  Implied Risk-Neutral Probability Density Functions from Option Prices: Theory and Application , 1997 .

[17]  Menachem Brenner,et al.  Implied foreign exchange rates using options prices , 1996 .

[18]  Thomas F. Coleman,et al.  Reconstructing the unknown volatility function , 1998 .

[19]  J. Cochrane,et al.  Beyond Arbitrage: 'Good Deal' Asset Price Bounds in Incomplete Markets , 1996 .

[20]  William R. Melick,et al.  Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis , 1997, Journal of Financial and Quantitative Analysis.

[21]  P. H. Kevin Chang,et al.  ERM Realignment Risk and its Economic Determinants as Reflected in Cross‐rate Options , 1998 .

[22]  Victor Isakov,et al.  The inverse problem of option pricing , 1997 .

[23]  Tie Su,et al.  Implied Volatility Skews and Stock Index Skewness and Kurtosis Implied by S&P 500 Index Option Prices , 1997 .

[24]  Merton H. Miller,et al.  Prices for State-contingent Claims: Some Estimates and Applications , 1978 .

[25]  F. Longstaff.  Option Pricing and the Martingale Restriction , 1995 .

[26]  S. Ross,et al.  Option pricing: A simplified approach☆ , 1979 .

[27]  Olivier Ledoit,et al.  Relative Pricing of Options with Stochastic Volatility , 1998 .

[28]  David S. Bates.  The Crash of ʼ87: Was It Expected? The Evidence from Options Markets , 1991 .

[29]  Dilip B. Madan,et al.  Pricing S&P 500 Index Options Using a Hilbert Space Basis , 1997 .

[30]  Tie Su,et al.  SKEWNESS AND KURTOSIS IN S&P 500 INDEX RETURNS IMPLIED BY OPTION PRICES , 1996 .

[31]  M. Osborne.  Brownian Motion in the Stock Market , 1959 .

[32]  Andrew W. Lo,et al.  Nonparametric estimation of state-price densities implicit in financial asset prices , 1995, Proceedings of 1995 Conference on Computational Intelligence for Financial Engineering (CIFEr).

[33]  Stylianos Perrakis,et al.  A Jumping Smile , 1997 .

[34]  Rama Cont.  Beyond implied volatility , 1998 .

[35]  R. Tompkins.  Implied volatility surfaces: uncovering regularities for options on financial futures , 2001 .

[36]  J. Campa,et al.  Implied Exchange Rate Distributions: Evidence from OTC Option Markets , 1997 .

[37]  M. Rockinger,et al.  Reading Interest Rate and Bond Futures Options' Smiles: How PIBOR and Notional Operators Appreciated the 1997 French Snap Election , 1998 .

[38]  P. Buchen,et al.  The Maximum Entropy Distribution of an Asset Inferred from Option Prices , 1996, Journal of Financial and Quantitative Analysis.

[39]  Mark Rubinstein,et al.  Edgeworth Binomial Trees , 1998 .

[40]  M. Rubinstein.,et al.  Recovering Probability Distributions from Option Prices , 1996 .

[41]  Rama Cont,et al.  Service de Physique de l’État Condensé, Centre d’études de Saclay , 1997 .

[42]  M. Rubinstein..  Nonparametric tests of alternative option pricing models using all reported trades and quotes on the , 1985 .

[43]  S. Posner,et al.  Valuing Exotic Options by Approximating the SPD with Higher Moments , 1998 .

[44]  James N. Bodurtha,et al.  Nonparametric estimation of an implied volatility surface , 1999 .

[45]  Leif Andersen,et al.  The equity option volatility smile: an implicit finite-difference approach , 1997 .

[46]  David S. Bates.  Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options , 1998 .

[47]  Lars E. O. Svensson,et al.  New Techniques to Extract Market Expectations from Financial Instruments , 1997 .

[48]  Emanuel Derman,et al.  STOCHASTIC IMPLIED TREES: ARBITRAGE PRICING WITH STOCHASTIC TERM AND STRIKE STRUCTURE OF VOLATILITY , 1998 .

[49]  Bruce Mizrach,et al.  Did Option Prices Predict the ERM Crises , 1996 .

[50]  Roger Symon,et al.  Reconciling the differences. , 1975 .

[51]  S. Ross.  Options and Efficiency , 1976 .

[52]  Gurdip Bakshi,et al.  Empirical Performance of Alternative Option Pricing Models , 1997 .

[53]  Dilip B. Madan,et al.  DETERMINING VOLATILITY SURFACES AND OPTION VALUES FROM AN IMPLIED VOLATILITY SMILE , 2001 .

[54]  Charles P. Thomas,et al.  The sovereignty option: the Quebec referendum and market views on the Canadian dollar , 1996 .

[55]  K. Toft.,et al.  Constructing Binomial Trees From Multiple Implied Probability Distributions , 1999 .

[56]  D. Madan,et al.  Estimation of risk-neutral and statistical densities by Hermite polynomial approximation: with an application to Eurodollar futures options , 1996 .

[57]  Olivier Ledoit,et al.  Gain, Loss, and Asset Pricing , 2000, Journal of Political Economy.

[58]  Mark Britten-Jones,et al.  Option Prices, Implied Price Processes, and Stochastic Volatility , 2000 .

[59]  David S. Bates.  Post-&Apos;87 Crash Fears in S&P 500 Futures Options , 1997 .

[60]  N. L. Johnson,et al.  Systems of frequency curves generated by methods of translation. , 1949, Biometrika.

[61]  David S. Bates.  Testing Option Pricing Models , 1995 .

[62]  P. H. Kevin Chang,et al.  Arbitrage-Based Tests of Target-Zone Credibility: Evidence from ERM Cross-Rate Options , 1998 .

[63]  Marco Avellaneda,et al.  Calibrating Volatility Surfaces Via Relative-Entropy Minimization , 1996 .

[64]  M. Rockinger,et al.  Reading the Smile: The Message Conveyed by Methods Which Infer Risk Neutral Densities , 1997 .

[65]  Michael Rockinger,et al.  Density-embedding Functions , 1997 .

[66]  A. Lo,et al.  Nonparametric Risk Management and Implied Risk Aversion , 2000 .

[67]  José Manuel Campa,et al.  Options-based analysis of emerging market exchange rate expectations: Brazil's real plan, 1994-1999, An , 2000 .

[68]  Menachem Brenner,et al.  No-Arbitrage Option Pricing: New Evidence on the Validity of the Martingale Property , 1997 .

[69]  Bruno Dupire.  Pricing with a Smile , 1994 .

[70]  M. Rubinstein..  Implied Binomial Trees , 1994 .

[71]  P. Garcia,et al.  Recovering probabilistic information from option markets: Tests of distributional assumptions , 1996 .

[72]  Allan M. Malz.  Estimating the Probability Distribution of the Future Exchange Rate from Option Prices , 1997 .

[73]  R. Engle,et al.  Option Hedging Using Empirical Pricing Kernels , 1997 .

[74]  Eric Jondeau,et al.  Reading Interest Rate and Bond Futures Options' Smiles Around the 1997 French Snap Election , 1998 .

[75]  Nusret Cakici,et al.  How to Grow a Smiling Tree , 1998 .

[76]  Goldman,et al.  Implied Trinomial Trees of the Volatility Smile , 1996 .

[77]  Douglas T. Breeden,et al.  Prices of State-Contingent Claims Implicit in Option Prices , 1978 .

[78]  Jens Carsten Jackwerth,et al.  Generalized Binomial Trees , 1996 .

[79]  Eric Jondeau,et al.  Estimating Gram-Charlier Expansions Under Positivity Constraints , 1999 .