Perturbation Methods in Credit Derivatives

CHAPTER 17Machine Learning

17.1 TRENDS IN QUANTITATIVE FINANCE RESEARCH

17.1.1 Some Recent Trends

Every so often an idea rips through the quantitative finance research community like a hurricane, turning careers on their heads and causing consultants to re‐badge themselves with new credentials which will qualify them for the new roles for which financial institutions are seeking to recruit. A couple of decades ago, perturbation methods were the new kids on the block, with the SABR model of Hagan et al. [2002] sweeping before it the previous wisdom that only exact analytic solutions were worthy of consideration as alternatives to full numerical solutions. The interest in the pioneering asymptotic analyses of Hagan et al. [2002] and Fouque et al. [2000] was driven mainly by an aspiration to be able to calibrate models efficiently in the presence of local‐stochastic volatility, in the absence of exact analytic formulae such as Black–Scholes for liquid option prices (and of the levels of computational power available today).

In the wake of the credit crunch of 2007, the focus was increasingly on dealing with regulation and finding efficient ways of performing the calculations which needed to be performed repeatedly to comply with them. A concomitant increase in the focus on counterparty default risk led to controversies over discrepancies between different discounting and funding curves, which fuelled the creation of a cottage industry referred to generically as XVA, with the ...