Abstract:
We develop a general method to infer martingale equivalent probability density functions (PDFs) for
asset prices using American options prices. The early exercise feature of American options precludes
expressing the option price in terms of the PDF of the price of the underlying asset. We derive tight
bounds for the option price in terms of the PDF and demonstrate how these bounds, together with
observed option prices, can be used to estimate the parameters of the PDF. We infer the distribution
for the price of crude oil during the Persian Gulf crisis and find the distribution differs significantly
from that recovered using standard techniques.
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