Related papers: Parallel Pricing Algorithms for Multi--Dimensional…
A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…
We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
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…
In this paper, we price American-style Parisian down-and-in call options under the Black-Scholes framework. Usually, pricing an American-style option is much more difficult than pricing its European-style counterpart because of the…
There is a vast literature on numerical valuation of exotic options using Monte Carlo, binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it…
Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…
This paper sets up a methodology for approximately solving optimal investment problems using duality methods combined with Monte Carlo simulations. In particular, we show how to tackle high dimensional problems in incomplete markets, where…
We present a high-performance budgeted multi-level Monte Carlo method for estimates on the entire spatial domain of multi-PDE problems with random input data. The method is designed to operate optimally within memory and CPU-time…
In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or…
This paper addresses an important gap in rigorous numerical treatments for pricing American options under correlated two-asset jump-diffusion models using the viscosity solution framework, with a particular focus on the Merton model. The…
This paper explores alternative regression techniques in pricing American put options and compares to the least-squares method (LSM) in Monte Carlo implemented by Longstaff-Schwartz, 2001 which uses least squares to estimate the conditional…
For pricing American options, %after suitable discretization in space and time, a sequence of discrete linear complementarity problems (LCPs) or equivalently Hamilton-Jacobi-Bellman (HJB) equations need to be solved in a sequential…
In the paper, the pricing of Quanto options is studied, where the underlying foreign asset and the exchange rate are correlated with each other. Firstly, we adopt Bayesian methods to estimate unknown parameters entering the pricing formula…
In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option…
Within a Markovian complete financial market, we consider the problem of hedging a Bermudan option with a given probability. Using stochastic target and duality arguments, we derive a backward numerical scheme for the Fenchel transform of…
We present a Monte-Carlo simulation algorithm for real-time policy improvement of an adaptive controller. In the Monte-Carlo simulation, the long-term expected reward of each possible action is statistically measured, using the initial…
This study presents a comparative analysis of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods in the context of derivative pricing, emphasizing convergence rates and the curse of dimensionality. After a concise overview of traditional…
The rough Bergomi (rBergomi) model, introduced recently in [5], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits with empirical implied…
Asynchronous iterations arise naturally in parallel computing if one wants to solve large problems with a minimization of the idle times. This paper presents an original model of asynchronous iterations for a time-domain decomposition…