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Perturbations Methods and the Costs of Regulatory Compliance

Written by Colin Turfus, Quantitative Analyst at Deutsche Bank. Colin will be presenting "Innovative Risk Modelling Approaches for FRTB & CCAR" at Global Derivatives in May, 2017.

One of the significant issues faced by banks as a consequence of regulatory initiatives such as FRTB and CCAR is a considerable increase in the amount of scenario calculation required for compliance. An immediate challenge is to put in place the infrastructure which in the case of FRTB has to be up and running by the end of 2019. A further issue is the computational challenge of meeting the requirement of more stringent risk reporting as frequently as daily.

A key consideration in implementing solutions is deciding which risk factors risk models should seek to capture: if too few are used in comparison with the pricing models used by the desk, hedges made based on the pricing models may appear inadequate and, e.g., increased capital charges may be levied; but if all potentially relevant risk factors are included in risk models, risk calculations can become prohibitively expensive to perform. A compromise solution where risk factors can be incorporated to an adequate degree into risk models at a cost which is less that of using the full pricing models would appear to be desirable.

As I mentioned in a blog here last year on the subject, perturbation methods which are drawing an increasing amount of attention in the quantitative finance research literature and at the Global Derivatives event offer just the sort of compromise needed where a degree of accuracy is traded for greater ease of computation, so “[providing] an easy way of assessing the potential impact of a particular model feature such as a correlation, counterparty risk or jumps.”

One of the main long-standing applications of perturbation methods is through the SABR model which allows the impact of stochastic volatility on the prices of vanilla products to be estimated to a good degree of accuracy without recourse to time-consuming numerical computation. More recently such methods have been applied also to more exotic derivatives including interest rate and credit derivatives. Likewise local volatility has been subjected to similar analyses.

From the risk management point of view, potentially more important is the impact of stochastic rates and/or credit intensity: it is rarely possible with standard modelling approaches to assess their impact on derivative prices without resorting to time-consuming Monte Carlo or PDE-based methods. Also, failure to incorporate these risk factors can in the presence of significant correlation result in important wrong-way risk being overlooked, something regulators are increasingly concerned to avoid. However recently developed perturbation-based approaches have revealed how such wrong-way risks can often be quantified to a good degree of accuracy with simple Black-Scholes type formulae (see e.g.

Expect to see more on perturbation methods in the months and years ahead.

Read more about Global Derivatives here.

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