We present in our work a continuous time Capital Asset Pricing Model where the volatilities of the market index and the stock are both stochastic. Using a singular perturbation technique, we provide approximations for the prices of european options on both the stock and the index. These...

In this paper, we establish a model for market making in options whose underlying is perfectly liquid. In our model framework, the stock price follows a generic stochastic volatility model under the real-world probability measure P. Market participants price options on this stock under a...

The question addressed in this paper is the performance of the optimal strategy, and the impact of partial information. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein-Uhlenbeck process. We focus on the optimal strategy with a...

In this paper, we present a continuous time Capital Asset Pricing Model where the volatilities of the market index and the stock are both stochastic. Using a singular perturbation technique, we provide approximations for the prices of European options on both the stock and the index. We derive...

In this paper, we revisit the "Smile Dynamics" problem. In a previous work, Bergomi built a class of linear stochastic volatility models in which he specified the joint dynamics between the underlying and its instantaneous forward variances. The author introduced a quantity, which he called the...

In this paper, we establish a model for market making in options whose underlying is perfectly liquid. In our model framework, the stock price follows a generic stochastic volatility model under the real-world probability measure P. Market participants price options on this stock under a...