In this paper we consider Fourier transform techniques to efficiently compute the Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss random variable, characterized by having a computable generalized characteristic function. We exploit the property of these risk measures of being the solution of an elementary optimization problem of convex type in one dimension for which Fast and Fractional Fourier transform can be implemented. An application to univariate loss models driven by L´evy or stochastic volatility risk factors dynamic is finally reported.
Ramponi, A. (2016). On a transform method for the efficient computation of conditional VaR (and VaR) with application to loss models with jumps and stochastic volatility. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 18(2), 575-596 [10.1007/s11009-015-9446-7].
On a transform method for the efficient computation of conditional VaR (and VaR) with application to loss models with jumps and stochastic volatility
RAMPONI, ALESSANDRO
2016-01-01
Abstract
In this paper we consider Fourier transform techniques to efficiently compute the Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss random variable, characterized by having a computable generalized characteristic function. We exploit the property of these risk measures of being the solution of an elementary optimization problem of convex type in one dimension for which Fast and Fractional Fourier transform can be implemented. An application to univariate loss models driven by L´evy or stochastic volatility risk factors dynamic is finally reported.File | Dimensione | Formato | |
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