Discussion Papers, Department of Business and Management Science, Norwegian School of Economics (NHH)
Knut K. Aase
The perpetual American put option for jump-diffusions: Implications for equity premiums
Abstract: In this paper we solve an optimal stopping problem with an
infinite time horizon, when the state variable follows a jump-diffusion.
Under certain conditions our solution can be interpreted as the price of an
American perpetual put option, when the underlying asset follows this type
The probability distribution under the risk adjusted
measure turns out to depend on the equity premium, which is not the case
for the standard, continuous version. This difference is utilized to find
intertemporal, equilibrium equity premiums.
We apply this technique to
the US equity data of the last century, and find an indication that the
risk premium on equity was about two and a half per cent if the risk free
short rate was around one per cent. On the other hand, if the latter rate
was about four per cent, we similarly find that this corresponds to an
equity premium of around four and a half per cent.
The advantage with
our approach is that we need only equity data and option pricing theory, no
consumption data was necessary to arrive at these conclusions.
market models are studied at an increasing level of complexity, ending with
the incomplete model in the last part of the paper.
Keywords: Optimal exercise policy; American put option; perpetual option; optimal stopping; incomplete markets; equity premiums; CCAPM; (follow links to similar papers)
JEL-Codes: D52; (follow links to similar papers)
36 pages, December 17, 2004
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