Related papers: Deep Least Squares Monte Carlo methods for the val…
A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic…
Stochastic versions of recursive integrated climate-economy assessment models are essential for studying and quantifying policy decisions under uncertainty. However, as the number of state variables and stochastic shocks increases, solving…
In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of…
In this paper, we adopt the least squares Monte Carlo (LSMC) method to price time-capped American options. The aforementioned cap can be an independent random variable or dependent on asset price at random time. We allow various time caps.…
Multilevel Monte Carlo (MLMC) is a recently proposed variation of Monte Carlo (MC) simulation that achieves variance reduction by simulating the governing equations on a series of spatial (or temporal) grids with increasing resolution.…
We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the…
In this paper we explore ways of numerically computing recursive dynamic monetary risk measures and utility functions. Computationally, this problem suffers from the curse of dimensionality and nested simulations are unfeasible if there are…
Consider Least Squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (2001) for pricing American style securities. This algorithm is based on the projection of the value of continuation onto a certain set of basis…
Under the Solvency II regime, life insurance companies are asked to derive their solvency capital requirements from the full loss distributions over the coming year. Since the industry is currently far from being endowed with sufficient…
We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. The algorithm is formulated for an arbitrary number of assets and…
The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in stochastic optimal stopping theory. In this work, we propose a quantum LSM based on…
This study investigates the application of machine learning algorithms, particularly in the context of pricing American options using Monte Carlo simulations. Traditional models, such as the Black-Scholes-Merton framework, often fail to…
A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the policy life plus the remaining account balance at maturity, regardless of 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…
In the following paper we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of…
The optimal stopping problem is a category of decision problems with a specific constrained configuration. It is relevant to various real-world applications such as finance and management. To solve the optimal stopping problem,…
We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo…
Multilevel Monte Carlo (MLMC) reduces the total computational cost of financial option pricing by combining SDE approximations with multiple resolutions. This paper explores a further avenue for reducing cost and improving power efficiency…
Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general,…
The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to…