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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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