International Journal of Theoretical and Applied Finance

I show that the structure of the firm is not neutral with respect to regulatory capital budgeted under rules which are based on the Value-at-Risk. Indeed, when a holding company has the liberty to divide its risk into as many subsidiaries as needed, and when the subsidiaries are subject to capital requirements according to the Value-at-Risk budgeting rule, then there is an optimal way to divide risk which is such that the total amount of capital to be budgeted by the shareholder is zero. This result may lead to regulatory arbitrage by some firms.

Over the past two decades Value-at-Risk (VaR) became arguably the most popular measure of financial risk. Major banks calculate VaR on daily basis in order to determine the amount of capital a bank needs to offset the market risk. Banks use calculation methods of their choice, and many estimations are based on the assumption that portfolio rates of return have normal distribution. The important question is whether the chosen method of VaR calculation is accurate. As the light-tail property of the normal distribution can cause significant underestimation of VaR, the Basel Committee suggested to calculate the amount of capital needed by multiplying the bank's internal estimate of VaR by the factor 3. It's also common to use the so-called "square root of time" rule when evaluating VaR over a longer time horizon. This article aims to refine Stahl's argument behind the "factor 3" rule and say a word of caution concerning the "square root of time" rule.

Since the energy markets liberalization at the beginning of the 1990s in Europe, electricity monopolies have gone through a profound evolution process. From an industrial organization point of view, they lost their monopoly on their historical business, but gained the capacity to develop in any sector. Companies went public and had to upgrade their financial risk management process to international standards and implement modern risk management concepts and reporting processes (VaR, EaR…). Even though important evolutions have been accomplished, we argue here that the long-term risk management process of utility companies has not yet reached its full maturity and is still facing two main challenges. The first one concerns the time consistency of long-term and mid-term risk management processes. We show that consistencies issues are coming from the different classical financial parameters carrying information on firms' risk aversion (cost of capital and short-term risk limits) and the concepts inherited from the monopoly period, like the loss of load value, that are still involved in the utility company decision-making process. The second challenge concerns the need for quantitative models to assess their business model. With the deregulation, utilities have to address the question of their boundaries. Although intuition can provide insights on the benefits of some firm structures like vertical integration, only sound and tractable quantitative models can bring answers to the optimality of different possible firm structures.

We study the simplest discrete-time finite-maturity model in which default arises when the firm is not able to pay its debt obligation using the current cash-flow plus the corporate liquidity. An important distinction is made between liquidity and solvency of the firm. The corporate financial policy is simultaneously defined by the dividend policy, and the leverage policy (the coupon and the principal of the bond). When the corporate financial policy implies no default risk and no taxes, we show that the corporate financial policy is irrelevant and this irrelevance result holds for any probability measure. When the corporate financial policy implies now some default risk, we show that the value of the firm is a piecewise decreasing function of the dividend policy for any leverage policy, so that dividend policy affects the value of the firm. However, shareholders may not always have the incentives to implement this optimal dividend policy. We show that when the value of the assets is low, shareholders have an incentive to deviate from this optimal dividend policy, and we also study the resulting agency costs. We finally compare the resulting quantities of our model to the base case suggested by Huang and Huang (2003).

The goal of the paper is the numerical analysis of the performance of Monte Carlo simulation based methods for the computation of credit-portfolio loss-distributions in the context of Markovian intensity models of credit risk. We concentrate on two of the most frequently touted methods of variance reduction in the case of stochastic processes: importance sampling (IS) and interacting particle systems (IPS) based algorithms. Because the subtle differences between these methods are often misunderstood, as IPS is often regarded as a mere particular case of IP, we describe in detail the two kinds of algorithms, and we highlight their fundamental differences. We then proceed to a detailed comparative case study based on benchmark numerical experiments chosen for their popularity in the quantitative finance circles.

Because of its very general formulation, the local volatility model does not have an analytical solution for European options. In this article, we present a new methodology to derive closed form solutions for the price of any European options. The formula results from an asymptotic expansion, terms of which are Black-Scholes price and related Greeks. The accuracy of the formula depends on the payoff smoothness and it converges with very few terms.