Download or read book A New Framework to Estimate the Risk-Neutral Probability Density Functions Embedded in Options Prices written by Mr.Kevin C. Cheng and published by International Monetary Fund. This book was released on 2010-08-01 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the widely-used double-lognormal approach by Bahra (1997), this paper presents a multi-lognormal approach with restrictions to extract risk-neutral probability density functions (RNPs) for various asset classes. The contributions are twofold: first, on the technical side, the paper proposes useful transformation/restrictions to Bahra’s original formulation for achieving economically sensible outcomes. In addition, the paper compares the statistical properties of the estimated RNPs among major asset classes, including commodities, the S&P 500, the dollar/euro exchange rate, and the US 10-year Treasury Note. Finally, a Monte Carlo study suggests that the multi-lognormal approach outperforms the double-lognormal approach.