Credit Risk & Volatility Modeling: New Approaches & Faster Calibration
A latest model for pricing bonds based on credit rating transitions, developed by Pietro Rossi of Prometeia and researchers at several Italian universities, is now in use at an unnamed insurance company. The model addresses a gap in existing financial tools, which typically focus on the probability of default rather than the more nuanced shifts in credit ratings.
Rossi, also an adjunct professor of computational finance at the University of Bologna, explained that the model creates “a stochastic scenario for transition matrices” allowing for the reproduction of observable bond prices based on their ratings. Credit transition matrices map the probabilities of a bond’s rating moving up, down, or remaining stable over a given period. The approach estimates bond prices not just at maturity, but at monthly intervals throughout the bond’s life.
The primary applications, according to Rossi, include calculating the distribution of present value for a credit portfolio’s profit and loss, and simulating the rating composition of a credit portfolio. The work was detailed in a paper published in January.
Beyond credit risk, Rossi and his collaborators have also focused on volatility modeling. Earlier this month, they published a paper detailing a faster calibration technique for models used to price options on the S&. P 500 and the VIX index. This new method bypasses the computational demands of traditional Monte Carlo simulations by utilizing deep neural networks to “learn” both S&P volatility and Vix volatility, significantly accelerating the calibration process.
The calibration problem – fitting a volatility model to both the S&P volatility surface and the volatility curve implied by the Vix index – has been a focus for quantitative analysts for roughly a decade, including researchers such as Julien Guyon, Mathieu Rosenbaum, and Jim Gatheral. Rossi acknowledged that the intellectual challenge of this problem is a significant motivator for the quant community.
Rossi’s solution was developed with Fabio Baschetti of the University of Verona and Giacomo Bormetti of the University of Pavia. According to a February 4, 2026 post on Risk.net, the technique allows for real-time joint calibration of SPX and VIX options.
Looking ahead, Rossi indicated two main research areas. One involves a critical examination of widely used interest rate models, specifically testing the accuracy of the SABR model. The other builds on the credit rating transition work, investigating whether the stochastic transition framework can be applied to price Bermudan or American options on defaultable bonds using least-squares Monte Carlo methods. Results from these investigations could be published in Risk.net in the near future.
Pietro Rossi is also Vicepresident of Prometeia Advisor Sim and President of the publishing houses Il Mulino and Carocci, according to Prometeia’s website.