Related papers: Monte Carlo Simulation for Trading Under a L\'evy-…
Simple Monte Carlo is a versatile computational method with a convergence rate of $O(n^{-1/2})$. It can be used to estimate the means of random variables whose distributions are unknown. Bernoulli random variables, $Y$, are widely used to…
In this paper, we consider a Monte Carlo simulation method (MinMC) that approximates prices and risk measures for a range $\Gamma$ of model parameters at once. The simulation method that we study has recently gained popularity [HS20, FPP22,…
This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number…
Finding Bertram's optimal trading strategy for a pair of cointegrated assets following the Ornstein--Uhlenbeck price difference process can be formulated as an unconstrained convex optimization problem for maximization of expected profit…
Consider a multivariate L\'evy-driven Ornstein-Uhlenbeck process where the stationary distribution or background driving L\'evy process is from a parametric family. We derive the likelihood function assuming that the innovation term is…
The pricing of financial derivatives, which requires massive calculations and close-to-real-time operations under many trading and arbitrage scenarios, were largely infeasible in the past. However, with the advancement of modern computing,…
In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of the Boltzmann equation to the case of kinetic models arising in the study of multiagent systems. For these phenomena, where…
We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk criterion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the…
Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. To this end, in this paper we present exact and…
We consider the problem of pricing path-dependent options on a basket of underlying assets using simulations. As an example we develop our studies using Asian options. Asian options are derivative contracts in which the underlying variable…
Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been…
Properties of the self-adjusted Monte Carlo algorithm applied to 2d Ising ferromagnet are studied numerically. The endogenous feedback form expressed in terms of the instant running averages is suggested in order to generate a biased random…
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…
For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…
In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for…
When stock prices are observed at high frequencies, more information can be utilized in estimation of parameters of the price process. However, high-frequency data are contaminated by the market microstructure noise which causes significant…
An important family of stochastic processes arising in many areas of applied probability is the class of L\'evy processes. Generally, such processes are not simulatable especially for those with infinite activity. In practice, it is common…
We introduce a stacking version of the Monte Carlo algorithm in the context of option pricing. Introduced recently for aeronautic computations, this simple technique, in the spirit of current machine learning ideas, learns control variates…
With the goal to provide absolute lower bounds for the best possible running times that can be achieved by $(1+\lambda)$-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes…
In this paper we address the problem of rare-event simulation for heavy-tailed L\'evy processes with infinite activities. We propose a strongly efficient importance sampling algorithm that builds upon the sample path large deviations for…