It is well-known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes  we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices.
It is well known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. In the present paper we consider the inverse problem, that is, given prices of perpetual American options for different strikes , we show how to construct a time-homogeneous stock price model which reproduces the given option prices.
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well-known
well known
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i.e.
that is,
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,
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model for the stock price
stock price model