Podcast: Pietro Rossi on credit ratings and volatility models

Stochastic approaches and calibration speed improve established models in credit and equity

Pietro Rossi had a problem. An insurance company needed a model that could price bonds based on the likelihood of changes in credit ratings. The standard, off-the-shelf models are based on probability of default – not, specifically, credit rating moves.

So, he – together with a team from Bologna-based consultancy Prometeia – built his own.

The resulting model, which is detailed in a January paper, is in production at the client’s business, says Rossi, adjunct professor of computational finance at the University of Bologna. 

“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 says.

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Credit transition matrices indicate the probability of a rating moving up, moving down or staying the same. Credit ratings are plotted along the horizontal and vertical axes. The largest probabilities are normally positioned along the diagonal of the matrix, suggesting the most likely scenario is that in the next period a bond will maintain its current rating. The elements outside the diagonal indicate the probabilities of a change in rating. 

In the approach Rossi and co-authors developed, the pricing is based on scenarios simulated using stochastic multi-period credit rating transition matrices. That allows bond prices to be estimated not only at maturity but also at intermediate monthly steps throughout the life of the portfolio. 

The main applications the team envisages are computing the distribution of the present value of a credit portfolio’s P&L and simulating the rating composition of a credit portfolio.

Related

Bridging credit transitions and spread dynamics 

Neural networks unleashed: joint SPX/VIX calibration has never been faster 

But credit risk is not all that Rossi has turned his talents to recently. He also published a paper earlier this month on volatility models and their calibration to S&P and Vix options. 

The work deploys a faster calibration technique than previous models. “It’s a technical contribution on how to calibrate the path-dependent volatility model proposed by Julien Guyon and Jordan Lekeufack,” explains Rossi. 

Rossi’s solution – developed with co-authors Fabio Baschetti of the University of Verona and Giacomo Bormetti of the University of Pavia – proposes to bypass the computational bottleneck from Monte Carlo simulations. “We can teach a network to learn both [SPX volatility and Vix volatility], so the calibration procedure is lightning fast,” Rossi says. 

The calibration of a volatility model so that it fits both the S&P volatility surface and the volatility curve implied by the Vix index has been attracting the attention of quants for about a decade, including Guyon, Mathieu Rosenbaum and Jim Gatheral. Rossi admits the intellectual challenge is a major draw for the quant community – possibly more so than the practical aspects of the problem.

Looking ahead, Rossi says he is pursuing two main research directions. One is a closer examination of widely used interest rate models, testing the correctness of the SABR model introduced by Hagan and others.

The other area is connected to the work on credit rating transition. Rossi and academic colleagues are investigating whether the stochastic transition framework can be used to price Bermudan or American options on defaultable bonds using least‑squares Monte Carlo. Either could become a Risk paper soon.

Index:

00:00 Introduction

01:41 Background on credit and rating transition

04:00 Uses of the stochastic approach 

07:45 Applications and calibration

15:10 Joint calibration of S&P and Vix options

17:50 Speed-up from previous methods

23:10 Why quants want to solve the joint calibration problem

29:35 Future projects

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