BFS 2002

Poster Presentation

Volatility time and properties of option prices

Johan Tysk, Svante Janson

We use a notion of stochastic time, called volatility time, to show convexity of option prices in the underlying asset if the contract function is convex as well as continuity and monotonicity of the option price in the volatility. Earlier results on the convexity of option prices require the volatility to be differentiable, or at least Lipschitz, in the underlying asset. Using the volatility time, we show that the volatility does not even need to be continuous in time and only needs to satisty a local Hölder condition in the underlying asset. Our method also yields new results on the continuity of option prices in the volatility.