Disentangling demand and supply in credit developments: A survey-based analysis for Italy

This paper combines qualitative information from the Eurosystem Bank Lending Survey with micro-data on loans for the participating Italian banks to assess the role of supply and demand factors in lending to enterprises developments, with a focus on the 2007-2009 financial crisis. Both demand and supply have played a relevant role, in the whole sample period and during the crisis. A counterfactual exercise shows that the effect of supply factors on the growth of lending was strongest after the Lehman collapse. On average, over the crisis period the negative effect on the annualized quarter-on-quarter growth rate of the panel banks’ lending to enterprises can be estimated in a range of 2.3-3.1 percentage points, depending on the specification. About one fourth of the total supply effect can be attributed to costs related to the banks’ balance sheet position, the rest to their perception of credit risk.     

Local volatility under rough volatility

Several asymptotic results for the implied volatility generated by a rough volatility model have been obtained in recent years (notably in the small-maturity regime), providing a better understanding of the shapes of the volatility surface induced by rough volatility models, supporting their calibration power to SP500 option data. Rough volatility models also generate a local volatility surface, via the so-called Markovian projection of the stochastic volatility. We complement the existing results on implied volatility by studying the asymptotic behavior of the local volatility surface generated by a class of rough stochastic volatility models, encompassing the rough Bergomi model. Notably, we observe that the celebrated “1/2 skew rule” linking the short-term at-the-money skew of the implied volatility to the short-term at-the-money skew of the local volatility, a consequence of the celebrated “harmonic mean formula” of [Berestycki et al. (2002). Quantitative Finance, 2, 61–69], is replaced by a new rule: the ratio of the at-the-money implied and local volatility skews tends to the constant $1/(H+3/2)$ (as opposed to the constant 1/2), where H is the regularity index of the underlying instantaneous volatility process.