We extend the model presented in Bonollo et al. by introducing a multiscenario framework that allows for a richer and more realistic specification, including non-static (stochastic) probabilities of default and losses given default. Though more complex from a computational point of view, the...

We show that VAR calculation speedup of an order of magnitude can be obtained using Smart Monte Carlo with a sophisticated interpolator. As a byproduct, we give some encouraging numerical results for evaluating N-dimensional Gaussian integrals without doing any integrals at all

We present a stochastic simulation model for estimating forward-looking corporate probability of default and loss given default. We formulate the model in a discrete time frame, apply capital-budgeting techniques to define the relationships that identify the default condition, and solve the...

We solve a moment problem to compute the best upper and lower bounds on the expected value E[φ(X)], subject to constraints E[X^i] = μ_i for i = 1, 2,...,n. By setting φ(x)=I_(-\inf,t], the indicator function for the event X ≤ t, we calculate the bounds on Pr(X ≤ t) = E[I_(-\inf,t]]. The...

The standard approach to discretizing VARs uses tensor grids. However, when the VAR components exhibit significant unconditional correlations or when there are more than a few variables, this approach creates large inefficiencies because some discretized states will be visited with only...

Modified Value-at-Risk (mVaR) and Modified Expected Shortfall (mES) are risk estimators that can be calculated without modelling the distribution of asset returns. These modified estimators use skewness and kurtosis corrections to normal distribution parametric VaR and ES formulas to reduce bias...

[Update: Within four weeks of the original publication of this research report, Risk Magazine reported in its 28th February 2012 issue story titled 'Goodbye VaR? Basel to Consider Other Risk Metrics': "A review of trading book capital rules, due to be launched in March by the Basel Committee on...

Assuming a Constant Elasticity of Variance (CEV) model for the asset price, that is a defaultable asset showing the so called leverage effect (high volatility when the asset price is low), a VaR constraint reevaluated over time induces an agent more risk averse than a logarithmic utility to take...

Its conceptual appeal has made the Conditional Value at Risk (CoVaR) one of the most influential systemic risk indicators. Despite its popularity, an outstanding methodological challenge may hamper the CoVaRs’ accuracy in measuring the time-series dimension of systemic risk. The dynamics of...

We test the naive model to forecast ex-ante Value-at-Risk (VaR) using a shrinkage estimator between realized volatility estimated on past return time series, and implied volatility quoted on the market. Implied volatility is often indicated as the operators expectation about future risk, while...