Related papers: Pricing Derivatives under Self-Exciting Dynamics: …
The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the…
We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…
A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…
We introduce a new class of processes for the evaluation of multivariate equity derivatives. The proposed setting is well suited for the application of the standard copula function theory to processes, rather than variables, and easily…
In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of piecewise deterministic Markov processes. In this…
In the present paper we present a finite element approach for option pricing in the framework of a well-known stochastic volatility model with jumps, the Bates model. In this model the asset log-returns are assumed to follow a…
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a regime-switching market driven by an underlying continuous- time…
We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the…
We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbounded intensity, not of L\'evy-driven type…
We consider a Markov process $X$, which is the solution of a stochastic differential equation driven by a L\'{e}vy process $Z$ and an independent Wiener process $W$. Under some regularity conditions, including non-degeneracy of the…
By using absolutely continuous lower bounds of the L\'evy measure, explicit gradient estimates are derived for the semigroup of the corresponding L\'evy process with a linear drift. A derivative formula is presented for the conditional…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
The aim of this paper is to introduce a new formalism for the deterministic analysis associated with backward stochastic differential equations driven by general c{\`a}dl{\`a}g martingales. When the martingale is a standard Brownian motion,…
The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically…
Designing efficient and rigorous numerical methods for sequential decision-making under uncertainty is a difficult problem that arises in many applications frameworks. In this paper we focus on the numerical solution of a subclass of…
We consider a 2-dimensional marked Hawkes process with increasing baseline intensity in order to model prices on electricity intraday markets. This model allows to represent different empirical facts such as increasing market activity,…
Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and…
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We…
We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk…
An extension of non-deterministic processes driven by the random telegraph signal is introduced in the framework of "piecewise deterministic Markov processes" [Davis], including a broader category of random systems. The corresponding…