Target volatility option pricing

In this paper we present two methods for the pricing of Target Volatility Options (TVOs), a recent market innovation in the field of volatility derivative. 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 asset minus the strike, floored at zero, scaled by the ratio of the target volatility (an arbitrary constant) and the realized volatility of the underlying over the life of the option. TVOs are popular with investors and hedgers because they are typically cheaper than their vanilla equivalent. We present two approaches for the pricing of TVOs: a power series expansion and a Laplace transform method. We also provide both model dependent and model independent solutions. The pricing methodologies have been tested numerically and results are provided.