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An Econometric Model for Option Price with Implications for Investors' Expectations and Audacity

Econometrica 1969 37(4), 685
It will be convenient to consider in detail one specific form of security option: common stock purchase warrants. The model to be constructed can be extended mutatis mutanidis to any convertible security; Section 4 explicitly relates the model of warrant price to convertible bond price. A common stock purchase warrant is a security which the holder may exchange, at his option, for equity capital. The exchange may be effected by surrendering the warrant and a prespecified sum of money before a prespecified date to the corporation issuing the common stock. The act of conversion is usually called the exercise of the warrant, and the accompanying money the exercise price. Let X be the price of a unit of common, let Y be the price of a warrant, and let A be the exercise price of Y. For the remainder of this study, we shall measure X and Y in units of A so that Y/A = y is the price of 1/A warrants and X/A = x is the price of 1/A common shares. In this way, y plus $1 can be converted into shares