Abstract
This is a compact report on desultory researches stretching over more than a decade.
Acknowledgment is made to the Carnegie Corporation for research aid, but sole responsibility for the results is mine.
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Notes
- 1.
These graphs show the general pattern of warrant pricing as a function of the common stock price (where units have been standardized to make the exercise price unity). The longer the warrant’s life T, the higher is F(X, T). For fixed T, T(X, T) is a convex function of X. In Fig. 11.1a, the perpetual warrant’s price is equal to that of the stock, with \(F(X,\infty )\) falling on OZ; it never pays to exercise such a warrant. In Fig. 11.1b, the points C 1, C 4, C 25, and \(C_{\infty }\) on AB are the points at which it pays to convert a warrant with T = 1, 4, 25 and \(\infty \) years to run. Note that \(F(X,\infty )\) is much less than X in this case. The pattern of Fig. 11.1b will later be shown to result from the hypothesis that a warrant must have a mean yield β greater than the stock’s mean yield α.
- 2.
Acknowledgment is made to F. Skilmore for these computations.
- 3.
The partial support of the Office of Naval Research and of the National Science Foundation, NSF G-19684, is gratefully acknowledged.
- 4.
Samuelson’s notation for this is F(X, T).
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Samuelson, P.A. (2015). Rational Theory of Warrant Pricing. In: Grünbaum, F., van Moerbeke, P., Moll, V. (eds) Henry P. McKean Jr. Selecta. Contemporary Mathematicians. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-22237-0_11
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