Before revision:  Following this new idea, we devise a general martingale structure for the price process, and obtain an inverse-Fourier pricing equation for claims paying at maturity a function of the asset value and its realized volatility. Thus with a single formula we are able to capture prices for derivatives depending on either an asset or its volatility , but also joint payoffs are allowed , like the target volatility option (TVO) , which shall be discussed.
After revision:  Following this new idea, we devise a general martingale structure for a single formula we are able to capture prices for derivatives depending on either an asset or its volatility , but also joint payoffs are allowed , like the target volatility option (TVO) , which shall be discussed.