The use of power numeraires in option pricing

Power numeraires are defined. They are applied to the Black-Scholes model and the drift of the stock is derived. It is also shown how to use them to derive formulas for power options with barriers. A reinterpretation of contour-shifting in the context of characteristic function pricing is given. It is shown how to use power numeraires to improve the convergence of the COS method and numerical results are presented.