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 About Donald

Don founded Kamakura Corporation in April 1990 and currently serves as its chairman and chief executive officer where he focuses on enterprise wide risk management and modern credit risk technology. His primary financial consulting and research interests involve the practical application of leading edge financial theory to solve critical financial risk management problems. Don was elected to the 50 member RISK Magazine Hall of Fame in 2002 for his work at Kamakura. Read More

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An Introduction to Derivative Securities, Financial Markets, and Risk ManagementAdvanced Financial Risk Management, 2nd ed.

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Kamakura Blog


This paper analyzes the number and the nature of factors driving the movements in the U.S. Treasury yield curve from January 2, 1962 through December 31, 2018. The process of model implementation reveals a number of important insights for interest rate modeling generally. First, model validation of historical yields is important because those yields are the product of a third-party curve fitting process that may produce spurious indications of interest rate volatility. Second, quantitative measures of smoothness and international comparisons of smoothness provide a basis for measuring the quality of simulated yield curves.

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Jens Hilscher, Robert A. Jarrow, and Donald R. van Deventer§

This paper derives a tractable, arbitrage-free valuation model for corporate coupon bonds that includes a more realistic recovery rate process than that used in the existing literature. The existing literature uses a recovery rate process that is misspecified because it includes the recovery rates for coupons to be paid after the default date. Pricing errors resulting from assuming recovery on coupons can be substantial in size. They are larger if recovery rates, coupons, maturity and default probabilities are larger. We present evidence that market prices of traded coupon bonds reflect the different recovery rates that our model predicts and that our model provides a good fit to market prices.

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This is the third of three attempts to justify the use of 158-year-old credit ratings in the credit portfolio management process.  In part 1 of this series, we showed that the use of historical ratings-based default rates severely overstates credit risk among all rated firms world-wide for the first 4 years.  For years 5 through 10, the use of historical default rates dramatically understates credit risk.  In part 2 of the series, we showed that trying to use ratings as a proxy for modern big data-based default probabilities failed as well, since the 20 ratings grades explained less than 38% of the variation in Kamakura Risk Information Services default probabilities at every maturity tested.  In this installment, we change the focus to traded bond spreads in the hope that ratings provide higher explanatory power for spreads and bond valuation. 

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It is common practice among credit analysts to use historical default rates published by rating agencies as a proxy for a true forward-looking firm-by-firm set of modern corporate default probabilities. Part 1 of this series showed that such approximations of true portfolio losses are grossly inaccurate. In this installment of our three-part series, we try to remedy the situation by replacing historical default rates associated with credit ratings over the last quarter of a century with forward-looking “big data” default probabilities that represent best practice.

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It is common practice among credit analysts to use historical default rates published by rating agencies as a proxy for a true forward-looking firm-by-firm set of modern corporate default probabilities.  This analysis shows that such approximations of true portfolio losses are grossly inaccurate. In the current environment, historical losses reported by rating agencies overstate near-term losses and seriously underestimate long-run losses.

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