A new model developed by an Italian computational finance expert and his team is offering a more nuanced approach to pricing bonds based on credit risk, moving beyond traditional reliance on probability of default. Pietro Rossi, adjunct professor at the University of Bologna, and consultants at Prometeia have created a system that factors in the likelihood of changes in credit ratings, a critical element often overlooked by standard models.
The model, detailed in a January paper, is already in production at an unnamed insurance company client, according to Rossi. “We realised that it was possible to build a framework where you create a stochastic scenario for transition matrices and … reproduce prices of observable bonds according to their actual ratings,” he explained in a recent podcast interview.
Credit transition matrices are central to the innovation. These matrices map the probabilities of a credit rating moving up, down, or remaining stable over a given period. Typically, the highest probabilities reside along the diagonal, indicating a bond is most likely to maintain its current rating. However, the model’s strength lies in its ability to simulate scenarios using these matrices over multiple periods, allowing for price estimations not just at maturity, but at intermediate points – monthly, for example – throughout the bond’s life.
This capability has significant implications for financial institutions managing credit portfolios. The team envisions applications including calculating the distribution of the present value of a portfolio’s profit and loss, and simulating the evolving rating composition of a credit portfolio over time. Essentially, it provides a more dynamic and granular view of risk.
The development comes as the financial industry continues to grapple with the complexities of credit risk modeling. A recent LinkedIn post by Joseph Breeden highlighted the limitations of existing approaches, arguing that current models, even those incorporating machine learning, often fail to adequately connect credit risk to financial outcomes. Breeden, author of a forthcoming book on redesigning credit risk analytics, contends that the focus should shift from generating credit scores to directly optimizing pricing and cut-off scores based on economic scenarios and cash flow calculations.
Rossi’s work also extends beyond credit risk. He recently published a separate paper focusing on volatility models, specifically addressing the challenge of calibrating path-dependent volatility models proposed by Julien Guyon and Jordan Lekeufack. The new technique offers a significantly faster calibration process than previous methods.
“It’s a technical contribution on how to calibrate the path-dependent volatility model,” Rossi stated. The solution, developed with collaborators Fabio Baschetti of the University of Verona and Giacomo Bormetti of the University of Pavia, bypasses computational bottlenecks associated with Monte Carlo simulations. By “teaching a network to learn” both S&P volatility and Vix volatility, the calibration process is dramatically accelerated.
The joint calibration of S&P and Vix options has been a longstanding challenge for quantitative analysts, attracting attention from figures like Julien Guyon, Mathieu Rosenbaum, and Jim Gatheral. Rossi acknowledges the intellectual appeal of the problem, suggesting it may be as motivating for quants as its practical applications.
Looking ahead, Rossi and his colleagues are pursuing further research in two key areas. One involves a rigorous examination of widely used interest rate models, specifically testing the validity of the SABR model. The other builds upon the credit rating transition framework, exploring whether it can be used to price Bermudan or American options on defaultable bonds using least-squares Monte Carlo methods. The results of these investigations could potentially lead to further publications in leading financial journals.
The podcast interview also touched on the applications of the model, with Rossi noting the potential for computing the distribution of the present value of a credit portfolio’s P&L and simulating the rating composition of a credit portfolio. The ability to model these scenarios provides a more comprehensive understanding of potential financial outcomes.
