Related papers: A Quantization Approach to the Counterparty Credit…

We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…

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…

This paper explores advancements in quantum algorithms for derivative pricing of exotics, a computational pipeline of fundamental importance in quantitative finance. For such cases, the classical Monte Carlo integration procedure provides…

An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on…

This paper provides a methodology for fast and accurate pricing of the long-dated contracts that arise as the building blocks of insurance and pension fund agreements. It applies the recursive marginal quantization (RMQ) and joint recursive…

In the design of software and cyber-physical systems, security is often perceived as a qualitative need, but can only be attained quantitatively. Especially when distributed components are involved, it is hard to predict and confront all…

The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive…

Risk allocation, the decomposition of a portfolio-wide risk measure into component contributions, is a fundamental problem in financial risk management due to the non-additive nature of risk measures, the layered organizational structures…

Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome…

A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…

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…

A positive correlation between exposure and counterparty credit risk gives rise to the so-called Wrong-Way Risk (WWR). Even after a decade of the financial crisis, addressing WWR in both sound and tractable ways remains challenging.…

Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…

This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes…

Measuring the corporate default risk is broadly important in economics and finance. Quantitative methods have been developed to predictively assess future corporate default probabilities. However, as a more difficult yet crucial problem,…

Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures…

There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B)…

Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a…

In this paper we use a hybrid Monte Carlo-Optimal quantization method to approximate the conditional survival probabilities of a firm, given a structural model for its credit defaul, under partial information. We consider the case when the…

Finance is one of the promising field for industrial application of quantum computing. In particular, quantum algorithms for calculation of risk measures such as the value at risk and the conditional value at risk of a credit portfolio have…