Perturbation methods in credit derivatives : strategies for efficient risk management

"Perturbation methods are currently seeing a surge of popularity, with Pat Hagan and collaborators generalising and extending their SABR approach to European option pricing (See for example Wilmott magazine, Managing Vol Surfaces, P. Hagan et al, 23 January 2018) and their methods being extended by various groups worldwide to cover more exotic options. The power of Green's function approaches is also being rediscovered. At the same time the increasing regulatory burden of ever more stress testing of models and of hedging strategies for market risk and counterparty risk puts computational efficiency at a premium. Financial institutions' default strategy of throwing everything into a big Monte Carlo simulation is reaching its limits with a premium on intelligent strategies allowing a trade-off, with the cost of introducing bespoke algorithms or approximations into risk calculations being compensated by a reduced computational burden. Perturbation methods provide a simple but widely applicable methodology for obtaining tractable but accurate analytic approximations useful for pricing of credit-contingent financial products and for risk management purposes such as XVA and exposure calculations."