A conditional independence approach for portfolio risk evaluation

Muromachi, Yukio

doi:10.21314/jor.2004.099

Cited by 8 publications

(7 citation statements)

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“…Even if we resort to quantum algorithms, estimating VaR contributions is hard, since the probability that the condition for the conditional expected value is satisfied affects the complexity, as we will see below. In light of this, we hereafter focus on CVaR contributions, only referring to some existing studies on VaR contribution calculation, such as the Monte Carlo method combined with importance sampling [26] and semi-analytical methods based on saddlepoint approximation [27][28][29].…”

Section: Risk Contributionsmentioning

confidence: 99%

Quantum algorithm for calculating risk contributions in a credit portfolio

Miyamoto¹

2022

Preprint

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Section: Risk Contributionsmentioning

confidence: 99%

Quantum algorithm for calculating risk contributions in a credit portfolio

Miyamoto¹

2022

Preprint

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“…Sometimes, we need to decompose the risk measures to contributions from the subgroups in the portfolio, in order to, for example, analyze concentration of the risk. There are some studies on how to define and calculate such risk contributions [21][22][23][24][25][26][27][28][29], which we now outline.…”

Section: Risk Contributionsmentioning

confidence: 99%

“…For example, it can notice that the risk concentrates on obligors in some specific industrial sector or some specific region, and that some business division in it are taking the risk too much. In fact, such measures called risk contributions have been defined and how to calculate them has been studied [5,[21][22][23][24][25][26][27][28][29]. They are written as conditional expected values, and therefore calculating them by Monte Carlo is more costly than the entire risk measures, since only a small fraction of samples matches the conditions and we need to generate more samples.…”

Section: Introductionmentioning

confidence: 99%

Quantum algorithm for calculating risk contributions in a credit portfolio

Miyamoto

2022

EPJ Quantum Technol.

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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 been proposed. In this paper, we focus on another problem in credit risk management, calculation of risk contributions, which quantify the concentration of the risk on subgroups in the portfolio. Based on the recent quantum algorithm for simultaneous estimation of multiple expected values, we propose the method for credit risk contribution calculation. We also evaluate the query complexity of the proposed method and see that it scales as $\widetilde{O} (\sqrt{N_{\mathrm{gr}}}/\epsilon )$ O ˜ ( N gr / ϵ ) on the subgroup number $N_{\mathrm{gr}}$ N gr and the accuracy ϵ, in contrast with the classical method with $\widetilde{O} (\log(N_{\mathrm{gr}})/\epsilon^{2} )$ O ˜ ( log ( N gr ) / ϵ 2 ) complexity. This means that, for calculation of risk contributions of finely divided subgroups, the advantage of the quantum method is reduced compared with risk measure calculation for the entire portfolio. Nevertheless, the quantum method can be advantageous in high-accuracy calculation, and in fact yield less complexity than the classical method in some practically plausible setting.

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“…For example, see Martin et al (2001) or Muromachi (2004). The VaR risk contribution formula in Martin et al (2001) is simple to apply and is nothing but the first order approximation.…”

Section: For More Information Where the Author Defines The Euler Contmentioning

confidence: 99%

“…The VaR risk contribution formula in Martin et al (2001) is simple to apply and is nothing but the first order approximation. On the other hand, the approximations provided in Muromachi (2004) are rather complex to compute. In particular, the expansions make use of an auxiliary function which acts like a CGF, and thus it is difficult to guarantee the existence of saddlepoints.…”

Section: For More Information Where the Author Defines The Euler Contmentioning

confidence: 99%