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 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...

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...

Local risk minimization is studied for the hedging of derivatives - a general (non quadratic) risk criterion is studied, and the optimality conditions are derived.

The normality of multi-asset returns in event time is shown empirically. A multivariate subordination mechanism is proposed in order to explain this phenomenon.

Credit risk - more specifically, default risk - is introduced in various classical models for option pricing. The consequences of this new parameter in terms of model calibration is studied.

This article aims at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since its name was coined in 1995 by merging the words "Economics" and "Physics", this new interdisciplinary field has grown in various directions: theoretical macroeconomics...

This article is the second part of a review of recent empirical and theoretical developments usually grouped under the heading Econophysics. In the first part, we reviewed the statistical properties of financial time series, the statistics exhibited in order books and discussed some studies of...