In this talk we shall present three approximation methods for the pricing of Target Volatility Options (TVOs), a recent market innovation in the field of volatility derivatives. TVOs allow investors to take a joint view on the future price of a given underlying (e.g. stocks, commodities, etc) and its realized volatility. For example, a target volatility call pays at maturity the terminal value of the underlying minus the strike, floored at zero, rescaled by the ratio of a given Target Volatility (an arbitrary constant) and the realized volatility of the underlying over the life of the option. TVOs are typically used by investors and hedgers to cheapen the price of an option or to leverage their exposure to the underlying.

We present three approaches for the pricing of TVOs: a power series expansion, a Laplace transform method and approximations based on Bernstein polynomials. The three approximations have been tested numerically and results are provided.