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Regulatory requirements dictate that financial institutions must calculate risk capital (funds that must be retained to cover future losses) at least annually. Procedures for doing this have been well-established for many years, but recent…
The Reduced-Basis Control-Variate Monte-Carlo method was introduced recently in [S. Boyaval and T. Leli\`evre, CMS, 8 2010] as an improved Monte-Carlo method, for the fast estimation of many parametrized expected values at many parameter…
Searching for new effective risk factors on stock returns is an important research topic in asset pricing. Factor modeling is an active research topic in statistics and econometrics, with many new advances. However, these new methods have…
In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
In the aftermath of the 2007 global financial crisis, banks started reflecting into derivative pricing the cost of capital and collateral funding through XVA metrics. Here XVA is a catch-all acronym whereby X is replaced by a letter such as…
We consider calculation of capital requirements when the underlying economic scenarios are determined by simulatable risk factors. In the respective nested simulation framework, the goal is to estimate portfolio tail risk, quantified via…
In the paper we develop mathematical tools of quantile hedging in incomplete market. Those could be used for two significant applications: o calculating the \textbf{optimal capital requirement imposed by Solvency II} (Directive 2009/138/EC…
This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number…
This article presents a stochastic framework to quantify the biometric risk of an insurance portfolio in solvency regimes such as Solvency II or the Swiss Solvency Test (SST). The main difficulty in this context constitutes in the proper…
We present Monte Carlo reconstruction, a new method for ``inverting'' observational data to constrain the form of the scalar field potential responsible for inflation. This stochastic technique is based on the flow equation formalism and…
The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on…
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.…
We provide a simple method to estimate the parameters of multivariate stochastic volatility models with latent factor structures. These models are very useful as they alleviate the standard curse of dimensionality, allowing the number of…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
We combine the one-dimensional Monte Carlo simulation and the semi-analytical one-dimensional heat potential method to design an efficient technique for pricing barrier options on assets with correlated stochastic volatility. Our approach…
We present a quantum algorithm that analyzes risk more efficiently than Monte Carlo simulations traditionally used on classical computers. We employ quantum amplitude estimation to evaluate risk measures such as Value at Risk and…
We examine a general multi-factor model for commodity spot prices and futures valuation. We extend the multi-factor long-short model in Schwartz and Smith (2000) and Yan (2002) in two important aspects: firstly we allow for both the long…
Determining risk contributions of unit exposures to portfolio-wide economic capital is an important task in financial risk management. Computing risk contributions involves difficulties caused by rare-event simulations. In this study, we…
This paper focuses on the study of an original combination of the Multilevel Monte Carlo method introduced by Giles [10] and the popular importance sampling technique. To compute the optimal choice of the parameter involved in the…