We develop a model for pricing securities whose value may depend simultaneously on equity, interest-rate, and default risks. The framework may also be used to extract probabilities of default (PD) functions from market data. Our approach is based entirely on observables such as equity prices and interest rates, rather than on unobservable processes such as firm value. The model stitches together in an arbitrage-free setting a CEV equity model (to represent the behavior of equity prices prior to default), a default intensity process, and a Heath-Jarrow-Morton model for the evolution of riskless interest rates. The model captures several stylized features such as a negative relation between equity prices and equity volatility, a negative relation between default intensity and equity prices, and a positive relationship between default intensity and equity volatility. We embed the model on a discrete-time, recombining lattice, making implementation feasible with polynomial complexity. We demonstrate the simplicity of calibrating the model to market data, and of using it to extract default information. The framework is extensible

Abstract This paper examines the role of repeat interactions between placement agents (investment banks) and investors in the initial pricing of convertible bonds. Under the assumption that attracting repeat investors can reduce search frictions in primary issue markets, we test the hypothesis that banks' relationships with investors actually allow more favorable pricing for issuing firms (in contrast to the "favoritism" hypothesis, under which banks use underpricing to reward favored clients). In the empirical analysis we also allow for a potentially important alternative channel through which search frictions might impact initial pricing: expected aftermarket liquidity. Using a sample of 601 Rule 144A issues for the years 1997-2007, we document robust negative relationships between at-issue discounts and both types of frictions. Our findings suggest that search frictions play a meaningful role in initial convertible bond pricing and, specifically, that intermediaries can add substantial value through repeated interactions with investors. Our results indicate that, with all other variables at their mean values, a deal with only 25% repeat investors will be priced at a 10.7% discount relative to fundamental value, while a deal with 75% repeat investors will be priced at a 7.1% discount. Given the mean deal size of $278 million, this translates to a potential savings of $10.2 million for the issuer. * We thank

1 We revisit the models developed in Das and Sundaram (2004) and Bandreddi, et al. (2007). Bandreddi, et al. (2007) use a simplified version of the model developed by Das and Sundaram for correlated default simulation. We find that in their setting, problematic probabilities may arise which may cause biased results for the purpose of default simulation and the pricing of derivative products. We suggest an alternative model — the D-CEV model, as an alternative to address this problem. The new model is an extension of a popular binomial model and is easy to implement. We further explore the natural characteristics of our alternative method with several numerical experiments. Our proposed model is found to resolve the unpleasant flaws in the model of Bandreddi, et al. (2007) while preserving its desirable properties. We also show how this framework accounts for several empirical features.