Articlegreen2003

Arbitrage-free estimation of the risk-neutral density from the implied volatility smile

58 citations0/0 files storedThe Journal of Computational Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

All methods for estimating the risk-neutral density from the volatility smile boil down to the completion of the implied volatility function by interpolating between available strike prices and extrapolating outside their range. In this paper we focus on the extrapolation and develop a new method, which is, under weak constraints, consistent with the absence of arbitrage. The method does not depend on a particular interpolation scheme and is therefore universally applicable. The implementation involves only straightforward numerical procedures. In an empirical study we apply the method to options on the German stock index DAX. The method turns out to be robust, accurate, and fast. Compared with the methods of Shimko (1993) and Bliss/Panigirtzoglou (2002), it tends to be superior.

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 2016“Options, Futures, and Other Derivatives”1987The Pricing of Options on Assets with Stochastic Volatilities 1976The valuation of options for alternative stochastic processes 1959Theory of Value 1978Prices of State-Contingent Claims Implicit in Option Prices 1973The Role of Securities in the Optimal Allocation of Risk-bearing 1996Recovering Probability Distributions from Option Prices

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2014Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints 2007Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity 2006Option-implied risk preferences: An extension to wider classes of utility functions 2007On extracting information implied in options 2008Stochastic Local Volatility 2010

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