Related papers: Pricing time-capped American options using Least S…
Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo…
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American…
This paper examines the valuation of American capped call options with two-level caps. The structure of the immediate exercise region is significantly more complex than in the classical case with constant cap. When the cap grows over time,…
We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We…
This paper is concerned with the solution of the optimal stopping problem associated to the valuation of Perpetual American options driven by continuous time Markov chains. We introduce a new dynamic approach for the numerical pricing of…
By leveraging the natural geometry of a smooth probabilistic system, Hamiltonian Monte Carlo yields computationally efficient Markov Chain Monte Carlo estimation. At least provided that the algorithm is sufficiently well-tuned. In this…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…
This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized…
We consider a multi-step algorithm for the computation of the historical expected shortfall such as defined by the Basel Minimum Capital Requirements for Market Risk. At each step of the algorithm, we use Monte Carlo simulations to reduce…
Monte Carlo methods, such as Markov chain Monte Carlo (MCMC), remain the most regularly-used approach for implementing Bayesian inference. However, the computational cost of these approaches usually scales worse than linearly with the…
We present a reduced basis method for the simulation of American option pricing. To tackle this model numerically, we formulate the problem in terms of a time dependent variational inequality. Characteristic ingredients are a POD-greedy and…
This article presents fast lower and upper estimates for a large class of options: the class of constrained multiple exercise American options. Typical options in this class are swing options with volume and timing constraints, and passport…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
Sequential Monte Carlo squared (SMC$^2$) methods can be used for parameter inference of intractable likelihood state-space models. These methods replace the likelihood with an unbiased particle filter estimator, similarly to particle Markov…
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least…
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,…
We introduce three related but distinct improvements to multilevel Monte Carlo (MLMC) methods for the solution of systems of stochastic differential equations (SDEs). Firstly, we show that when the payoff function is twice continuously…
We consider option hedging in a model where the underlying follows an exponential L\'evy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The…