Density and Distribution Evaluation for Convolution of Independent Gamma Variables

Several numerical evaluations of the density and distribution of convolution of independent gamma variables are compared in their accuracy and speed. In application to renewal processes, an efficient formula is derived for the probability mass function of the event count

Asymptotics of a Clustering Criterion for Smooth Distributions

We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed. The asymptotic behavior of the point at which the observations are split into two clusters is examined. The results obtained can then be utilized to construct an interval estimate of the point which splits the data and develop tests for bimodality and presence of clusters

Convexity Bias in the Pricing of Eurodollar Swaps

The traditional use of LIBOR futures prices to obtain surrogates for the Eurodollar forward rates is proved to yield a systematic bias in the pricing of Eurodollar swaps when one assumes that the yield curve is well described by the Heath-Jarrow-Morton model. The resulting theoretical inequality is consistent with the empirical observations of Burghardt and Hoskins (1995), and it provide a theoretical basis for price anomalies that are suggested by more recent empirical data

Buses, Bullies, and Bijections

The random—or orderly—seating of passengers on a bus is used to motivate several questions about cycles of permutations. These in turn motivates the investigation of bijections between special subsets of permutations. The goal, of course, is to give simple explanations of surprising facts

On the Convergence of Credit Risk in Current Consumer Automobile Loans

Loan seasoning and inefficient consumer interest rate refinance behavior are well-known for mortgages. Consumer automobile loans, which are collateralized loans on a rapidly depreciating asset, have attracted less attention, however. We derive a novel large-sample statistical hypothesis test suitable for loans sampled from asset-backed securities to populate a transition matrix between risk bands. We find all current risk bands eventually converge to a super-prime credit, despite remaining underwater. Economically, our results imply borrowers forwent \$1,153-\$2,327 in potential credit-based savings through delayed prepayment. We present an expected present value analysis to derive lender risk-adjusted profitability. Our results appear robust to COVID-19