Simone Scotti

An Optimal Dividend and Investment Control Problem under Debt Constraints

This paper concerns the problem of determining an optimal control on the dividend and investment policy of a firm under debt constraints. We allow the company to make investment by increasing its outstanding indebtedness, which would impact its capital structure and risk profile, thus resulting in higher interest rate debts. Moreover, a high level of debt is also a challenging constraint to any firm, as it is the threshold below which the firm value should never go to avoid bankruptcy. It is equally possible for the firm to divest parts of its business in order to decrease its financial debt owed to creditors. In addition, the firm may favor investment by postponing or reducing any dividend distribution to shareholders. We formulate this problem as a combined singular and multiswitching control problem and use a viscosity solution approach to get qualitative descriptions of the solution. We further enrich our studies with a complete resolution of the problem in the two-regime case and provide some numeric...

OPTIMAL CREDIT ALLOCATION UNDER REGIME UNCERTAINTY WITH SENSITIVITY ANALYSIS

We consider the problem of credit allocation in a regime-switching model. The global evolution of the credit market is driven by a benchmark, the drift of which is given by a two-state continuous-time hidden Markov chain. We apply filtering techniques to obtain the diffusion of the credit assets under partial observation and show that they have a specific excess return with respect to the benchmark. The investor performs a simple mean–variance allocation on credit assets. However, returns and variance matrix have to be computed by a numerical method such as Monte Carlo, because of the dynamics of the system and the non-linearity of the asset prices. We use the theory of Dirichlet forms to deal with the uncertainty on the excess returns. This approach provides an estimation of the bias and the variance of the optimal allocation, and return. We propose an application in the case of a sectorial allocation with Credit Default Swaps (CDS), fully calibrated with observable data or direct input given by the portfolio manager.

Alternative to beta coefficients in the context of diffusions

We develop an alternative to the beta coefficient of the CAPM theory. We show the link between this notion and the Wiener chaos expansion of the underlying processes. In the setting of Markov diffusions, we define the drift-neutral beta, which is the quantity of benchmark such that the resulting portfolio is immune to an infinitesimal change of drift on the Brownian motion driving the benchmark. Our approach yields a coefficient which in many practical cases depends on the initial values of both the portfolio and its benchmark. It can also be used to take into account extreme risks and not only the variance. We study several classical diffusion processes and give a full analysis in the case of Jacobi processes. Examples with credit indices show the efficiency of the method in hedging a portfolio.

Sensitivity Analysis for Marked Hawkes Processes - Application to CLO Pricing

This paper introduces a model for pricing Collateralized Loan Obligations, where the underlying credit risk is driven by a marked Hawkes process, involving both clustering effects on defaults and random recovery rates. We provide a sensitivity analysis of the CLO price with respect to the parameters of the Hawkes process using a change of probability and a variational approach. We also provide a simplified version of the model where the intensity of the Hawkes process is taken as the instantaneous default rate. In this setting, we give a moment-based formula for the expected survival probability.

Bid-ask spread modelling, a perturbation approach

Our objective is to study liquidity risk, in particular the so-called “bid-ask spread”, as a by-product of market uncertainties. “Bid-ask spread”, and more generally “limit order books” describe the existence of different sell and buy prices, which we explain by using different risk aversions of market participants. The risky asset follows a diffusion process governed by a Brownian motion which is uncertain. We use the error theory with Dirichlet forms to formalize the notion of uncertainty on the Brownian motion. This uncertainty generates noises on the trajectories of the underlying asset and we use these noises to expound the presence of bid-ask spreads. In addition, we prove that these noises also have direct impacts on the mid-price of the risky asset. We further enrich our studies with the resolution of an optimal liquidation problem under these liquidity uncertainties and market impacts. To complete our analysis, some numerical results will be provided.