In this paper the zero vanna implied volatility approximation for the price of freshly minted volatility swaps is generalized to seasoned volatility swaps. We also derive how volatility swaps can be hedged using a strip of vanilla options with Gaussian weights. For the family of stochastic...

The main assumption of the vanna-volga method is the existence of a flat but stochastic implied volatility for the pricing of vanilla options. Even though `flat but stochastic' appears to be self-contradictory, it is to an extent justified on empirical grounds. In this short note we argue that...

It is well-known that in normal stochastic volatility models with zero correlation the fresh volatility swap price is exactly equal to the at-the-money implied volatility. To replicate a volatility swap, however, the price of a volatility swap at inception is insufficient. Its price throughout...

A short review of the pricing of vanilla call and put options in stochastic volatility models with jump to default is given. Expressions are obtained that relate vanilla call and put options prices under pure stochastic volatility diffusion models to prices under stochastic volatility with jump...