Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and S{\o}lna (2011, CUP) analyzes models in which the...

We provide an analytical and flexible framework to evaluate incentive options. Our model not only considers vesting periods and trading and hedging restrictions on the holders, but also specifically includes provisions of reloading and resetting to capture the fact that firms tend to grant more...

We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling inert investors. With a suitable scaling, we show that...

Selected hedge funds employ trend-following strategies in an attempt to achieve superior risk-adjusted returns. We employ a lookback straddle approach for evaluating the return characteristics of a trend-following strategy. The strategies can improve investor performance in the context of a...

The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be integrated into the theoretical framework of convex...