We propose a new stochastic volatility model for pricing options on assets that exhibit seasonal trends in volatility. Such assets are prevalent among commodities, with futures on grains and energy being an example. The model is based on the 3/2 stochastic volatility model, but includes a...

In this paper, we develop asymptotic formulas for long-dated Foreign Exchange (FX) and swaptions implied volatilities. We extend the method exposed in Decamps and De Schepper (2009b) to a generic model with time-dependent parameters. Imposing a condition on the skew, we derive averaging formulas...

Under most local and stochastic volatility models the underlying forward is assumed to be a positive function of a time-changed Brownian motion. It relates nicely the implied volatility smile to the so-called activity rate in the market. Following Young and DeWitt-Morette (1986), we propose to...