Retrieving risk neutral densities based on risk neutral moments through a Gram-Charlier series expansion

In this paper we employ a new method to retrieve the risk neutral probability density function of future asset prices, or their implied log-returns, based on an exponential form of a Gram-Charlier series expansion, known as C-type. This type of expansion guarantees that the values of the risk neutral density will be always positive and it can account for strong deviations of the stock price distributions from the Gaussian. In a set of numerical and empirical applications, the paper shows the accuracy and versatility of the method for recovering the true risk neutral density.

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

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

[3]  Ximing Wu,et al.  Calculation of maximum entropy densities with application to income distribution , 2003 .

[4]  Dilip B. Madan,et al.  CONTINGENT CLAIMS VALUED AND HEDGED BY PRICING AND INVESTING IN A BASIS , 1994 .

[5]  G. Debreu,et al.  Theory of Value , 1959 .

[6]  Giuseppe Muscolino,et al.  Probability density function of MDOF structural systems under non-normal delta-correlated inputs , 1999 .

[7]  D. Madan,et al.  Spanning and Derivative-Security Valuation , 2000 .

[8]  R. Jarrow,et al.  APPROXIMATE OPTION VALUATION FOR ARBITRARY STOCHASTIC PROCESSES , 1982 .

[9]  K. Singleton.  Estimation of affine asset pricing models using the empirical characteristic function , 2001 .

[10]  A. Lo,et al.  Nonparametric Estimation of State‐Price Densities Implicit in Financial Asset Prices , 1998 .

[11]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[12]  K. Arrow.  The Role of Securities in the Optimal Allocation of Risk-bearing , 1964 .

[13]  M. Rockinger,et al.  Gram–Charlier densities , 2001 .

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

[15]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[16]  C. Charlier.  A New Form of the Frequency Function. , 1930 .

[17]  Yacine Ait-Sahalia,et al.  Nonparametric Option Pricing Under Shape Restrictions , 2002 .

[18]  Daniel Giamouridis,et al.  Estimating Implied PDFs From American Options on Futures: A New Semiparametric Approach , 2002 .

[19]  S. Ross,et al.  The valuation of options for alternative stochastic processes , 1976 .