Revealing the Implied Risk-Neutral MGF with the Wavelet Method

Options are believed to contain unique information about the risk- neutral moment generating function (MGF hereafter) or the risk-neutral probability density function (PDF hereafter). This paper applies the wavelet method to approximate the risk-neutral MGF of the under- lying asset from option prices. Monte Carlo simulation experiments are performed to elaborate how the risk-neutral MGF can be obtained using the wavelet method. The Black-Scholes model is chosen as the benchmark model. We offer a novel method for obtaining the implied risk-neutral MGF for pricing out-of-sample options and other complex or illiquid derivative claims on the underlying asset using information obtained from simulated data.

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

[2]  Antonios Antoniou,et al.  Price Clustering and Discreteness: Is There Chaos Behind the Noise? , 2004, cond-mat/0407471.

[3]  Nikolaos Panigirtzoglou,et al.  Testing the Stability of Implied Probability Density Functions , 2002 .

[4]  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).

[5]  Paul S. Addison,et al.  The Illustrated Wavelet Transform Handbook , 2002 .

[6]  Sharmishtha Mitra,et al.  A wavelet filtering based analysis of macroeconomic indicators: the Indian evidence , 2006, Appl. Math. Comput..

[7]  Fionn Murtagh,et al.  On neuro-wavelet modeling , 2004, Decis. Support Syst..

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

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

[10]  Connor Jeff,et al.  Wavelet Transforms and Commodity Prices , 2005 .

[11]  Allan M. Malz.  ESTIMATING T DISTRIBUTION QF THE FUTURE EXCHANGE RATE FROM OPTION , 1997 .

[12]  Barbara Hubbard,et al.  The World According to Wavelets , 1996 .

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

[14]  R. Gencay,et al.  An Introduction to Wavelets and Other Filtering Methods in Finance and Economics , 2001 .

[15]  Anestis Antoniadis,et al.  BAYESIAN ESTIMATION IN SINGLE-INDEX MODELS , 2004 .

[16]  Marina Vannucci,et al.  Bayesian Methods for Wavelet Series in Single-Index Models , 2005 .

[17]  Lei Gao,et al.  DETECT MARKET BASELINE TREND WITH WAVELET ANALYSIS , 2005 .

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

[19]  Chenghu Ma,et al.  Intertemporal recursive utility and an equilibrium asset pricing model in the presence of Lévy jumps , 2006 .

[20]  J. B. Ramsey,et al.  DECOMPOSITION OF ECONOMIC RELATIONSHIPS BY TIMESCALE USING WAVELETS , 1998, Macroeconomic Dynamics.

[21]  Enrico Capobianco,et al.  Independent component analysis and resolution pursuit with wavelet and cosine packets , 2002, Neurocomputing.

[22]  R. Davidson,et al.  Wavelet Analysis of Commodity Price BehaviorbyRussell , 1998 .

[23]  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.

[24]  J. B. Ramsey,et al.  The Decomposition of Economic Relationships by Time Scale Using Wavelets: Expenditure and Income , 1998 .

[25]  Charles K. Chui,et al.  An Introduction to Wavelets , 1992 .