Dipartimento di Scienze Statistiche

.The Solvency II regulatory regime provides the calculation of a capital requirement, the Solvency Capital Requirement (SCR), for the insurance and reinsurance companies, that is based on a market-consistent evaluation of the Basic Own Funds (BOF) probability distribution forecast over a one-year time horizon. The paper proposes the application of a stochastic model for ratingbased pricing of risky securities for the purpose of spread risk assessment and management in Solvency II framework, under an internal model or partial internal model. This model is an extended generalized Markov model for the term structure of credit spreads, proposed by Gambaro et al. (2018) and based on Lando (1998) and Jarrow, Lando and Turnbull (1997 and 2004), and it models the credit rating transitions and the default process using an extension of a time-homogeneous Markov chain and a subordinator process. The calibration methodology, consistent with the purpose of the paper, i.e. the assessment of spread risk, and with the market consistency required by Solvency II, uses an appropriate set of time series of credit spread term structures, differentiated by economic sector and rating class, and is based on the Particle Filter technique, in order to jointly estimate the real-world (necessary for risk assessment) and risk-neutral (necessary for pricing) parameters. Specifically, two calibration methodologies are proposed: a multi-rating one, based on the time series of all available rating classes credit spread term structures , and a singlerating, based on the time series of a single rating class credit spread term structures.