We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru (1991). We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix...

We introduce here for the first time the long-term swap rate, char- acterised as the fair rate of an overnight indexed swap with infinitely many exchanges. Furthermore we analyse the relationship between the long-term swap rate, the long-term yield, and the long-term simple rate, considered as...

We develop the HJM framework for forward rates driven by affine processes on the state space of symmetric positive semidefinite matrices. In this setting we find an explicit representation for the long-term yield in terms of the model parameters. This generalises the results of El Karoui et al....

We price for different affine stochastic volatility models some derivatives that recently appeared in the market. These products are characterised by payoffs depending on both stock and its volatility. Using a Fourier-analysis approach, we recover in a much simpler way some results already...

This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known in closed-form. Moreover, the basket...

A model describing the dynamics of a foreign exchange (FX) rate should preserve the same level of analytical tractability when the inverted FX process is considered. We show that affine stochastic volatility models satisfy such a requirement. Such a finding allows us to use affine stochastic...

We propose a quantization-based numerical scheme for a family of decoupled FBSDEs. We simplify the scheme for the control in Pagès and Sagna (2018) so that our approach is fully based on recursive marginal quantization and does not involve any Monte Carlo simulation for the computation of...

We present a flexible approach for the valuation of interest rate derivatives based on Affine Processes. We extend the methodology proposed in Keller-Ressel et al. (2009) by changing the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. We then...

We consider a short rate model, driven by a stochastic process on the cone of positive semidefinite matrices. We derive sufficient conditions ensuring that the model replicates normal, inverse or humped yield curves

We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed efficiently through the FFT...