相关论文: Monte Carlo Methods and Path-Generation techniques…
In this paper we introduce a new algorithm for American Monte Carlo that can be used either for American-style options, callable structured products or for computing counterparty credit risk (e.g. CVA or PFE computation). Leveraging least…
In this paper we propose and analyse a method for estimating three quantities related to an Asian option: the fair price, the cumulative distribution function, and the probability density. The method involves preintegration with respect to…
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…
Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques are applied for pricing and hedging representative financial instruments of increasing complexity. We compare standard Monte Carlo (MC) vs QMC results using Sobol' low…
We introduce a new method to calculate the credit exposure of European and path-dependent options. The proposed method is able to calculate accurate expected exposure and potential future exposure profiles under the risk-neutral and the…
Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to…
In this paper, we present a very fast Monte Carlo scheme for additive processes: the computational time is of the same order of magnitude of standard algorithms for Brownian motions. We analyze in detail numerical error sources and propose…
Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
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.…
In many financial applications Quasi Monte Carlo (QMC) based on Sobol low-discrepancy sequences (LDS) outperforms Monte Carlo showing faster and more stable convergence. However, unlike MC QMC lacks a practical error estimate. Randomized…
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…
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…
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random…
The calculation of option Greeks is vital for risk management. Traditional pathwise and finite-difference methods work poorly for higher-order Greeks and options with discontinuous payoff functions. The Quasi-Monte Carlo-based conditional…
This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…
Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios…
Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…
In this paper, we discuss a simple yet robust PDE method for evaluating path-dependent Asian-style options using the non-oscillatory forward-in-time second-order MPDATA finite-difference scheme. The valuation methodology involves casting…
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…