Discussion Papers, Department of Finance and Management Science, Norwegian School of Economics (NHH)
No 2005/11:
Using Option Pricing Theory to Infer About Equity Premiums
Knut K. Aase ()
Abstract: In this paper we make use of option pricing theory to
infer about historical equity premiums. This we do by comparing the prices
of an American perpetual put option computed using two different models:
The first is the standard one with continuous, zero expectation, Gaussian
noise, the second is a strikingly similar model, except that the zero
expectation noise is of Poissonian type. The interesting fact that makes
this comparison worthwhile, is that the probability distribution under the
risk adjusted measure turns out to depend on the equity premium in the
Poisson model, while this is not so for the standard, Brownian motion
version. This difference is utilized to find the intertemporal, equilibrium
equity premium. We apply this technique to the US equity data of the last
century and find that, if the risk free short rate was around one per cent,
this corresponds to a risk premium on equity about two and a half per cent.
On the other hand, if the risk free rate was about four per cent, we find
that this corresponds to an equity premium of around four and a half per
cent. The advantage with our approach is that we only need equity data and
option pricing theory, no consumption data was necessary to arrive at these
conclusions. We round off the paper by investigating if the procedure also
works for incomplete models.
Keywords: Historical equity premiums; perpetual American put option; equity premium puzzle; risk free rate puzzle; geometric Brownian motion; geometric Poisson process; CCAPM; (follow links to similar papers)
JEL-Codes: G00; (follow links to similar papers)
32 pages, November 30, 2005
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