Optimal capital structure and endogenous default

In a sequence of fascinating papers, Leland and Leland and Toft have investigated various properties of the debt and credit of a firm which keeps a constant profile of debt and chooses its bankruptcy level endogenously, to maximise the value of the equity. One feature of these papers is that the credit spreads tend to zero as the maturity tends to zero, and this is not a feature which is observed in practice. This defect of the modelling is related to the diffusion assumptions made in the papers referred to; in this paper, we take a model for the value of the firm's assets which allows for jumps, and find that the spreads do not go to zero as maturity goes to zero. The modelling is quite delicate, but it just works; analysis takes us a long way, and for the final steps we have to resort to numerical methods.     

Single and joint default in a structural model with purely discontinuous asset prices

Structural models of credit risk are known to present both vanishing spreads at very short maturities and a poor spread fit over longer maturities. The former shortcoming, which is due to the diffusive behaviour assumed for asset values, can be circumvented by considering discontinuous asset prices. In this paper the authors resort to a pure jump process of the Variance-Gamma type. First the authors calibrate the corresponding Merton type structural model to single-name data for the DJ CDX.NA.IG and CDX.NA.HY components. By so doing, they show that it also circumvents the diffusive structural models difficulties over longer horizons. Particularly, it corrects for the underprediction of low-risk spreads and the overprediction of high-risk ones. Then the authors extend the model to joint default, resorting to a recent formulation of the VG multivariate model and without superimposing a copula choice. They fit default correlation for a sample of CDX.NA names, using equity correlation. The main advantage of our joint model, with respect to the existing non-diffusive ones, is that it allows full calibration without the equicorrelation assumption, but still in a parsimonious way. As an example of the default assessments which the calibrated model can provide, the authors price an FtD swap.     

An approximate distribution of delta-hedging errors in a jump-diffusion model with discrete trading and transaction costs

We introduce a jump-diffusion model for asset returns with jumps drawn from a mixture of normal distributions and show that this model adequately fits the historical data of the S&P500 index. We consider a delta-hedging strategy (DHS) for vanilla options under the diffusion model (DM) and the proposed jump-diffusion model (JDM), assuming discrete trading intervals and transaction costs, and derive an approximation for the probability density function (PDF) of the profit-and-loss (P&L) of the DHS under both models. We find that, under the log-normal model of Black–Scholes–Merton, the actual PDF of the P&L can be well approximated by the chi-squared distribution with specific parameters. We derive an approximation for the P&L volatility in the DM and JDM. We show that, under both DM and JDM, the expected loss due to transaction costs is inversely proportional to the square root of the hedging frequency. We apply mean–variance analysis to find the optimal hedging frequency given the hedger's risk tolerance. Since under the JDM it is impossible to reduce the P&L volatility by increasing the hedging frequency, we consider an alternative hedging strategy, following which the P&L volatility can be reduced by increasing the hedging frequency.     

Investment and asset securitization with an option‐for‐guarantee swap

This article addresses the investment and financing decisions of entrepreneurs entering into option‐for‐guarantee swaps (OGSs). OGSs increase investment option value significantly. Entrepreneurs initially accelerate their investments and then postpone them as funding gaps grow. Guarantee costs increase with project risks when the funding gap is sufficiently small or large, but the opposite holds true otherwise. Investments are postponed when project risks, effective tax rates, or bankruptcy costs increase. Surprisingly, the higher the project risk, the more the entrepreneur will borrow, with a much higher leverage than predicted by classic models. Entrepreneurs can use OGSs to securitize their assets.     

On a risk model with dependence between interclaim arrivals and claim sizes

We consider an extension to the classical compound Poisson risk model for which the increments of the aggregate claim amount process are independent. In Albrecher and Teugels (2006 Albrecher, H. and Teugels, J. 2006. Exponential behavior in the presence of dependence in risk theory. Journal of Applied Probability, 43(1): 257–273. [Crossref], [Web of Science ®] , [Google Scholar]), an arbitrary dependence structure among the interclaim time and the subsequent claim size expressed through a copula is considered and they derived asymptotic results for both the finite and infinite-time ruin probabilities. In this paper, we consider a particular dependence structure among the interclaim time and the subsequent claim size and we derive the defective renewal equation satisfied by the expected discounted penalty function. Based on the compound geometric tail representation of the Laplace transform of the time to ruin, we also obtain an explicit expression for this Laplace transform for a large class of claim size distributions. The ruin probability being a special case of the Laplace transform of the time to ruin, explicit expressions are therefore obtained for this particular ruin related quantity. Finally, we measure the impact of the various dependence structures in the risk model on the ruin probability via the comparison of their Lundberg coefficients.