Dan Georgescu and Nicholas J. Higham
Correlation matrices arise in many applications to model the dependence between variables. Where there is incomplete or missing information for the variables, this may lead to missing values in the correlation matrix itself, and the problem of how to complete the matrix. We show that some of these practical problems can be solved explicitly, via simple formulae, and we explain how to use mathematical tools to solve the more general problem where explicit solutions may not exist. “Simple” is, of course, a relative term, and the underlying matrix algebra and optimization necessarily makes this article more mathematically sophisticated than the typical Bank Underground post.
Graeme Douglas, Nicholas Vause and Joseph Noss
Risky asset prices plummeted following the collapse of Lehman Brothers in 2008. Whilst driven partly by deteriorations in fundamental news, these falls were amplified by ‘flighty’ investors that sold at the first signs of trouble. Conventional wisdom dictates that life insurers, with their long-term investment horizons, are better placed than most to ‘lean against the wind’ by looking through short-term fluctuations in asset prices. They could thereby stabilise prices when others are selling. But the structure of regulations can greatly influence insurers’ investment incentives. Using our model of insurers’ asset allocations, we find that new ‘Solvency II’ regulations reduce UK life insurers’ willingness to act as the white knights of financial markets, particularly in the face of falling interest rates.
Neha Jain, James O’Reilly & Nicholas Silk
In 2020 Google plans to launch a self-driving car which has already driven nearly one million miles without causing an accident; it doesn’t get tired and irritable, swerve into lamp posts or require a driving test. The in-built chauffeur comes in the form of a rotating LIDAR laser taking 1.3 million recordings per second, and it’s a better driver than you. By eliminating the element of human blunders, driverless cars are forecast to reduce motor accidents by up to 90% in the US according to McKinsey. That might imply a substantial impact on the insurance industry, with liability potentially shifting to car manufacturers. Such developments would pose challenging questions for the PRA in regulating UK insurance firms.