We rely on high frequency data to explore the joint dynamics of underlying and option markets. In particular, high frequency data make observable the realized variance process of the underlying, so its effects on option price dynamics are tested. Empirical results are confronted with the...

We rely on high frequency data to explore the joint dynamics of underlying and option markets. In particular, high frequency data make observable the realized variance process of the underlying, so its effects on option price dynamics are tested. Empirical results are confronted with the...

<section xml:id="fut21644-sec-0001"> This study provides explicit formulas for the moments and the autocorrelation function of the number of jumps over a given interval for a self‐excited Hawkes process. These computations are possible thanks to the affine property of this process. Using these quantities an implementation of the...</section>

Order splitting is a standard practice in trading : traders constantly scan the limit order book and choose to limit the size of their market orders to the quantity available at the best limit, thereby controlling the market impact of their orders. In this article, we focus on the other trades,...

A limit order book provides information on available limit order prices and their volumes. Based on these quantities, we give an empirical result on the relationship between the bid-ask liquidity balance and trade sign and we show that liquidity balance on best bid/best ask is quite informative...

In this note, we cast a Hawkes process-based order book model into a markovian setting and; using techniques from the theory of Markov chains and stochastic stability, show that the order book is stable and leads to a diffusive price limit at large time scales.

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 note, I study further a new approach recently introduced for the hedging of derivatives in incomplete markets via non quadratic local risk minimization. A structure result is provided, which essentially shows the equivalence between non-quadratic risk minimization under the historical...

We study the influence of taking liquidity costs and market impact into account when hedging a contingent claim, first in the discrete time setting, then in continuous time. In the latter case and in a complete market, we derive a fully non-linear pricing partial differential equation, and...

We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with respect to boundary conditions on a multidimensional...