In this paper, we analyse options that are bought or sold by the company on whose stocks these options are written, leading to dilution and anti-dilution effects. We provide valuation equations for the European versions of such options, and discuss conditions for existence and uniqueness of their prices. Option prices to be paid or received for these options by the company are shown to be different from those that apply for standard options (which are bought and sold by outside investors). Since the options become part of the company's assets/liabilities, the stochastic process followed by the stock price changes. We demonstrate how the new stock price process can be derived, and discuss economic implications of our results. Numerical examples illustrate our findings.