This paper provides some initial findings on two issues arising from the extraction of PDFs. First, many heavily traded options are traded on listed exchanges with contracts expiring at fixed dates. This imparts a maturity dependence to summary statistics (e.g., moments or probabilities of being above or below a certain price) calculated from the PDFs implied by these options. That is, the summary statistics are limited in that there will only be as many observations as the number of days the option contract is traded (often a year at most), and the statistics will not be comparable because each applies to a slightly different maturity period. These limitations frustrate many attempts to make historical comparisons of summary statistics, or to use such statistics in time-series regression applications. Second, calculations from the PDFs are essentially point Confidence Intervals and ConstantMaturity Series for Probability Measures Extracted from Options Prices William Melick and Charles Thomas 294 Melick and Thomas estimates. To date, little work has been done to quantify the uncertainty around any point estimate generated from a PDF.
Confidence Intervals and ConstantMaturity Series for Probability Measures Extracted from Options PricesFaculty Publications
Citation Information"Confidence Intervals and Constant-Maturity Series for Probability Measures Extracted From Options Prices", with Charles Thomas, Information in Financial Asset Prices: Proceedings of a Conference held by the Bank of Canada, May 1998 edited by Kevin Clinton and Mark Zelmer, Bank of Canada, Ottawa, Ontario, Canada March 1999, pp. 293-320.