In view of their tractability, Hawkes processes are widely employed in high-frequency data. However, even in the absence of kernel (i.e. Poisson case), it is well-documented empirically that the baseline is not constant, reproducing in particular seasonalities from the financial market. In this...

We extend the discrete-time construction of [Guyon, J.: The Joint S&P 500/VIX Smile Calibration Puzzle Solved, Risk, April 2020] and explain how to build a continuous-time stochastic volatility (SV) model which jointly and exactly calibrates S&P 500 (SPX) smiles, VIX futures, and VIX smiles at...

We study graphon mean-field backward stochastic differential equations (BSDEs) with jumps and associated dynamic risk measures. We establish the existence, uniqueness and measurability of solutions under some regularity assumptions. For an interacting mean-field particle system with...

We show how traders use marketable limit orders (MLOs) to liquidate a position over a trading window when there is latency in the marketplace. MLOs are liquidity taking orders that specify a price limit and are for immediate execution only; however, if the price limit of the MLO precludes it...

This paper presents the binomial expansion and series with optimized binomial coefficients. The binomial series is built on the building blocks of optimized binomial coefficients and multiple summations of geometric series

This paper applies two statistical arbitrage algorithms on the U.S. equities market, using daily historical prices from January 2005 to March 2012. The algorithms construct portfolios using two different frameworks, namely, the Vasicek model and co-integration approach, with a Markov...

Hybrid equity-rate derivatives are commonly traded between financial institutions, but are challenging to price with traditional methods. Especially challenging are those contracts which involve an explicit interest rate (fixing) dependence in the cashflows, which stretches typical...

This paper demonstrates that the equilibrium dynamics of a continuous-time macro-finance model can be characterized by the probabilistic solution of a coupled forward-backward stochastic differential equation. The probabilistic approach can, to some extent, overcome the ``curse of...

We propose a new jump-diffusion process, the Heston-Queue-Hawkes (HQH) model, combining the well-known Heston model and the recently introduced Queue-Hawkes (Q-Hawkes) jump process. Like the Hawkes process, the HQH model can capture the effects of self-excitation and contagion. However, since...

We introduce and study the class of {\em CBI-time-changed Lévy processes} (CBITCL), obtained by time-changing a Lévy process with respect to an integrated continuous-state branching process with immigration (CBI). We characterize CBITCL processes as solutions to a certain stochastic integral...