| Speaker | Title | Time | Date | Place |
| Mark Schroder | Optimal debt contracts and product market competition with exit and entry | 10.30am | Friday 12/05/2008 | GSB 3.138 |
| Abstract: We show that optimal debt contracts in the presence of product market competition are typically different from standard debt contracts. We consider a market with two incumbents, one levered (target) and one with deep pocke (competitor). Renewal of target's debt depends on its profits, which are determined by the competitor's pricing strategy. When the competitor benefits from non-renewal of target's debt, it has incentive to price more aggressively. To counter this, bondholders make renewal less profit sensitive, and the optimal debt contract is smooth (nonkinked) and concave, and lies below the standard debt contract. Bondholders leave the limited liability constraint slack in a region of profits, and therefore appear to leave money on the table by failing to collect all profits when they fall short of the debt's face value. But this flattening of the contract results in higher profits for the levered firm for each state of demand, and a higher expected payout for bondholders. The larger the competitor's benefit from non-renewal, the flatter the contract. On the other hand, when the competitor benefits from renewal of the target's debt (say non-renewal results in target's replacement by a more efficient entrant), then the optimal debt contract is nonsmooth (sometimes taking the form of a binary option), and much more profit sensitive for some profit levels than the standard contract. This increased sensitivity amplifies the competitor's incentive to price less aggressively, resulting in higher profits for the levered firm and higher payout to bondholders. In either case, our results demonstrate -the optimal contract must be designed accounting for the impact of the contract itself on the profit function of the levered firm. Furthermore, bondholders prefer lending to weaker firms (firms whose competitors benefit from renewal) because the competitor's pricing incentive, amplified by the more profit sensitive contract, results in higher expected payouts. | ||||
| Steven Shreve Carnegie Mellon University | Double Skorokhod Map and Reneging Real-Time Queues | 1:30pm | Friday 12/05/2008 | RLM 9.166 |
| Abstract: An explicit formula for the Skorokhod map on [0,a] is provided. Specifically, it is shown that on the space of right-continuous functions with left limits taking values in the real numbers [a typographically complex formula goes here, see included paper below] is the unique function taking values in [0,a] that is obtained from the original by minimal "pushing'' at the endpoints 0 and a. An application of this result to real-time queues with reneging is outlined. This is joint work with L. Kruk, J. Lehoczky and K. Ramanan.
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| Huyen Pham University Paris 7 Diderot | Optimal portfolio/consumption choice in a liquidity risk model with random trading dates | 3:00 pm | Monday 12/01/2008 | RLM 9.166 |
| Abstract: We consider a portfolio/consumption choice problem in a market model with liquidity risk. The main feature is that the investor can trade and observe stock prices only at exogenous Poisson arrival times. These times model for example the arrival of buy/sell orders in an illiquid market. The agent may also consume continuously from his cash holdings, and his goal is to maximize his expected utility from consumption. This is a mixed discrete/continuous stochastic control problem, nonstandard in the literature. We first show how the dynamic programming principle leads to a coupled system of Integro-Differential Equations (IDE), and we prove an analytic characterization of this control problem by adapting the concept of viscosity solutions. Next, we derive smoothness results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second-order ODE. In the numerical part of this work, we provide a convergent numerical algorithm for the resolution to this coupled system of IDE. Several numerical experiments illustrate the impact of the restricted liquidity trading opportunities, and we measure in particular the utility loss with respect to the classical Merton consumption problem. We finally illustrate the behavior of optimal consumption policies between two trading dates. Based on joint works with: P. Tankov, F. Gozzi and A. Cretarola. | ||||
| Thomas Bielecki Illinois Institute of Technology | Up and Down Credit Risk | 1:30pm | Friday 11/07/2008 | RLM 9.166 |
| Abstract: This paper discusses the main modeling approaches that have been developed so far for handling portfolio credit derivatives. In particular the so called top, top down and bottom up approaches are discussed. We first provide an overview of these approaches. Then we give some mathematical insights to the fact that information, namely, the choice of a relevant model filtration, is the major modeling issue. In this regard, we examine the notion of thinning that was recently advocated for the purpose of hedging a multi-name derivative by single-name derivatives. We then give a further analysis of the various approaches using simple models, discussing in each case the issue of possibility of hedging. Finally we explain by means of numerical simulations (semi-static hedging experiments) why and when the portfolio loss process may not be a sufficient statistics for the purpose of valuation and hedging of portfolio credit risk. | ||||
| Gerard Brunick UT Austin | Generalizing the Local Volatility Approach to address Path-Dependent Options | 1:30pm | Friday 9/26/2008 | RLM 9.166 |
| Abstract: We briefly review the standard approach to local volatility models based upon the Fokker-Planck-Kolmogorov forward equation. We then introduce an alternative approach to the problem that avoids the use of PDE arguments. We will see that this new approach gives strictly stronger results than the PDE-based approach, and we will show how this new approach generalized to a relatively large class of path-dependent options, whereas the forward equation-based approach is essentially limited to European options. | ||||
| Gerard Brunick UT Austin | A Survey of the Stochastic Volatility Literature | 1:30pm | Friday 9/19/2008 | RLM 9.166 |
| Abstract: We will review some of the literature on stochastic volatility. We will discuss some of the "stylized facts" about market prices that we would like to reproduce in our model, and discuss the various approaches that have been developed to produce tractable models with "smirk" and "smile". | ||||