Contributions published at Quantitative Finance (Marc Chesney)

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Stochastic processes of common use in mathematical finance are presented throughout this book, which consists of eleven chapters, interlacing on the one hand financial concepts and instruments, such as arbitrage opportunities, admissible strategies, contingent claims, option pricing, default risk, ruin, and on the other hand, Brownian motion, diffusion processes, Lévy processes, together with the basic properties of these processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. Only basic knowledge of probability theory is assumed; the book is organized so that the mathematical facts pertaining to a given financial question are gathered close to the study of that question.

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This paper is concerned with clarifying the link between risk measurement and capital efficiency. For this purpose we introduce risk measurement as the minimum cost of making a position acceptable by adding an optimal combination of multiple eligible assets. Under certain assumptions, it is shown that these risk measures have properties similar to those of coherent risk measures. The motivation for this paper was the study of a multi-currency setting where it is natural to use simultaneously a domestic and a foreign asset as investment vehicles to inject the capital necessary to make an unacceptable position acceptable. We also study what happens when one changes the unit of account from domestic to foreign currency and are led to the notion of compatibility of risk measures. In addition, we aim to clarify terminology in the field.

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We study investment and disinvestment decisions in situations where there is a time lag 0 from the time t when the decision is taken to the time when the decision is implemented. Applying the probabilistic approach to the combined entry and exit decisions under the Parisian implementation delay, we solve the constrained maximization problem, obtaining an analytic solution to the optimal "starting" and "stopping" levels. We compare our results with the instantaneous entry and exit situation, and show that an increase in the uncertainty of the underlying process hastens the decision to invest or disinvest, extending a result of Bar-Ilan and Strange (1996).

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We propose a valuation method for financial assets subject to default risk, where investors cannot observe the state variable triggering the default but observe a correlated price process. The model is sufficiently general to encompass a large class of structural models and can be seen as a generalization of the model of Duffie and Lando (Econometrica 69:633–664, [2001]). In this setting we prove that the default time is totally inaccessible in the market’s filtration and derive the conditional default probabilities and the intensity process. Finally, we provide pricing formulas for default-sensitive claims and illustrate in particular examples the shapes of the credit spreads.

Luca Taschini outlines how collaboration between the academic and the business world has helped one company in the cement industry to tackle the EU emissions trading scheme.

The objective of this thesis is to consider different risk management issues in relation to operational risk with a special emphasis on terrorism risk. Our motivation to implement research in this particularly challenging area of risk management is due to the increasing magnitude of operational losses over the last decade and their negative effect on financial industry. This thesis contributes to the existing research on operational risk in several ways. First, our research suggests a model that addresses the issue of dependence between operational losses and how it can be accounted for in the value of capital charge for operational risk. Second, we provide a better understanding of the impact of a particular type of operational risk event, specifically of terrorist attacks . As evidenced by the 9/11 attacks, this risk can be catastrophic and can have negative consequences on the behavior of financial markets. We implement empirical analysis of the impact of terrorist attacks on stock, bond and commodity markets and suggest possible diversification strategies of terrorism risk. Finally, we contribute to the area of operational risk transfer, by developing a model for pricing of a multiple-event coupon paying CAT bond. The bond that we consider covers exposure to catastrophic risk such as natural and man-made disasters, including terrorist events.

This paper develops a continuous-time real options’ pricing model to study managers’ incentives to cheat in the presence of equity-based compensation plans. It shows that managers’ incentives to cheat are strongly influenced by the efficiency of the justice. The model’s main result is that managers have greater incentives to commit fraudulent actions under stock options than under common stocks based compensation plans.

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Market-based measures are currently very popular among policy makers. In a system for marketable permits, relevant companies exchange permits on the theory that trading creates economic incentives that encourage firms to minimize the costs to society of pollution control. The chief appeal of economic incentives as the regulatory device for achieving environmental standards is the potentially large cost-saving that they promise. The source of these cost savings is the capacity of economic instruments to take advantage of the large differentials abatement costs across polluters, as formally proved by [74]. In chapter 2, we review fundamental concepts in environmental economics and survey the main theoretical results regarding the use of emission permits. In an effort to bridge the gap between theory and observed market-price behavior, in chapter 3 we investigate the historical time series of the SO2 and CO2 emission permits price in the U.S. market and in the EU ETS, respectively. More precisely, we advocate the use of a new GARCH-type structure for the analysis of the returns of the permit price and demonstrate its effectiveness in terms of model fit and out-of-sample value-at-risk forecasting. Taking into account the most important features of the EU ETS, in chapter 4 we provide a simple conceptual framework and develop an equilibrium model for the price of the emission permits. This chapter is similar in spirit to [44] and [91] - two papers developed in parallel to our work. Unlike these two, this chapter gives insights into the dynamics of the CO2 permit price for a finite time horizon in presence of asymmetric information. In particular, the obtained equilibrium price for emission reflects the scarcity or excess of permits in the market. Finally, we introduce a CO2-option pricing model comparison. The comparison is carried out between the conventional Black, Merton and Scholes model and our equilibrium model. In the final chapter of the thesis, chapter 5, we evaluate when it is optimal to undertake a reversible investment to reduce noxious emissions or trading permits. In other words, we evaluate the price-level at which trading permits is a cheaper solution. In particular, I derive in analytic form the premium for the flexibility embedded in emission permits, extending the works of [22] and [5]. This preliminary result explains the different behavior of the premium for the flexibility of emission permits under both reversible and irreversible investment. Such a result has also extremely interesting and practical relevance for policy makers, as discussed in the chapter.

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This paper introduces a new filter, called least-squares (LS) filter, as an alternative to the widely used Hodrick-Prescott (HP) filter. The LS filter has two properties which distinguish it from the HP filter. First, the LS filter rather than the HP filter uses first differences as a measure of the smoothness of a nowhere differentiable random variable. Second, the LS filter rather than the HP filter uses a reference time series to avoid the subjective choice of weights.

This paper introduces a simple approach to classify corporate bonds. It relies entirely on the quoted price as well as on the quoted bid and ask price of corporate bonds. If current bond prices reflect all the relevant corporate information, then this approach is sufficient for a credit rating which is also up-to-date. We apply the approach outlined in the paper to the group of coupon-bearing bonds issued by banks as well as to other groups of corporate bonds including industrial companies and federal states. Our five-year experience shows that our algorithm works well, even for illiquid markets.

In this paper, we introduce a new algorithm to estimate the term structure of interest rates. It is obtained from a constrained optimization, where the objective is to minimize the integral of squared first derivatives of the instantaneous forward interest rate subject to the condition that the estimated bond prices lie within the range of observed bid and ask prices. We use a finite series of ordinary Laguerre polynomials to approximate the unknown function of the instantaneous forward interest rate. The objective function can be written explicitly as a quadratic form of the Laguerre constants and the nonlinear constraints can be obtained from a recurrence relationship. The estimation error is less than one basis point, given a sufficient number of bonds.

In this article, we describe the various sorts of American Parisian options and propose valuation formulae. Although there is no closed-form valuation for these products in the non-perpetual case, we have been able to reformulate their price as a function of the exercise frontier. In the perpetual case, closed-form solutions or approximations are obtained by relying on excursion theory. We derive the Laplace transform of the first instant Brownian motion reaches a positive level or, without interruption, spends a given amount of time below zero. We perform a detailed comparison of perpetual standard, barrier and Parisian options