Related papers: Sparse Grid Method for Highly Efficient Computatio…
In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities…
Exposure simulations are fundamental to many xVA calculations and are a nested expectation problem where repeated portfolio valuations create a significant computational expense. Sensitivity calculations which require shocked and unshocked…
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…
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…
We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo…
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…
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The…
This study contributes to understanding Valuation Adjustments (xVA) by focussing on the dynamic hedging of Credit Valuation Adjustment (CVA), corresponding Profit & Loss (P&L) and the P&L explain. This is done in a Monte Carlo simulation…
The focus of this paper is the efficient computation of counterparty credit risk exposure on portfolio level. Here, the large number of risk factors rules out traditional PDE-based techniques and allows only a relatively small number of…
Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all the trades with each counterparty under both market and credit risk. We present a multi-Gaussian process regression approach,…
Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for…
Risk budgeting is a portfolio strategy where each asset contributes a prespecified amount to the aggregate risk of the portfolio. In this work, we propose an efficient numerical framework that uses only simulations of returns for estimating…
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…
Valuation of Credit Valuation Adjustment (CVA) has become an important field as its calculation is required in Basel III, issued in 2010, in the wake of the credit crisis. Exposure, which is defined as the potential future loss of a default…
The Sharpe ratio is an important and widely-used risk-adjusted return in financial engineering. In modern portfolio management, one may require an m-sparse (no more than m active assets) portfolio to save managerial and financial costs.…
We use a replica approach to deal with portfolio optimization problems. A given risk measure is minimized using empirical estimates of asset values correlations. We study the phase transition which happens when the time series is too short…
We consider the problem of optimizing a portfolio of financial assets, where the number of assets can be much larger than the number of observations. The optimal portfolio weights require estimating the inverse covariance matrix of excess…
We propose a structural default model for portfolio-wide valuation adjustments (xVAs) and represent it as a system of coupled backward stochastic differential equations. The framework is divided into four layers, each capturing a key…
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…
Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality…