Contributions published at Quantitative Finance (Marc Chesney)

In this article the problem of the American option valuation in a Lévy process setting is analysed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps in the call case), known results concerning the currency option value as well as the exercise boundary are obtained with a martingale approach. With possible discontinuities of the underlying process at the exercise boundary (i.e. with positive jumps in the call case), original results are derived by relying on first passage time and overshoot associated with a Lévy process. For finite life American currency calls, the formula derived by Bates or Zhang, in the context of a negative jump size, is tested. It is basically an extension of the one developed by Mac Millan and extended by Barone‐Adesi and Whaley. It is shown that Bates' model generates pretty good results only when the process is continuous at the exercise boundary.

Many countries receive illegal migrants but are reluctant to accept them due to possible negative externalities. We provide a rationale for not policing illegal migration by linking it to the tourism industry. By paying illegal migrants less than local workers, the relative price of the non-traded goods is shown to be lower than it would be in the absence of such workers. An expansion in tourist trade, under certain intensity conditions, necessarily raises resident welfare and employment. This tourist boom necessarily lowers the welfare of the illegal migrants. It is established that an increase in tourism increases the supply of illegal migrants.

Within the context of investment under uncertainty, the real options literature has led to models that capture primarily the time to wait flexibility of monopolistic corporations' investment decision. In this paper, we propose an approach which relies on barrier options to model production and/or sales delocalization flexibility for multinational enterprises making decisions under exchange rate uncertainty. We then extend the model by introducing game theoretic considerations to show how the information set and the competitive structure of the market may lead firms to act strategically and exercise their delocalization options preemptively at an endogenously fixed exchange rate barrier.

In this paper, the problem of optimal timing, when to adopt an environmental policy in a strategic framework is considered. Using real options theory and some basic tools of game theory, we show that, under certain assumptions, a country behaving strategically should wait longer before adopting such a policy than if it behaves unstrategically or within a larger entity. Such a postponed decision is sub-optimal as regards to the environment protection.

Recent studies on global warming have introduced the inherent uncertainties associated with the costs and benefits of climate policies and have often shown that abatement policies are likely to be less aggressive or postponed in comparison to those resulting from traditional cost–benefit analyses (CBA). Yet, those studies have failed to include the possibility of sudden climate catastrophes. The aim of this paper is to account simultaneously for possible continuous and discrete damages resulting from global warming, and to analyse their implications on the optimal path of abatement policies. Our approach is related to the new literature on investment under uncertainty, and relies on some recent developments of the real option in which we incorporated negative jumps (climate catastrophes) in the stochastic process corresponding to the net benefits associated with the abatement policies. The impacts of continuous and discrete climatic risks can therefore be considered separately. Our numerical applications lead to two main conclusions: (i) gradual, continuous uncertainty in the global warming process is likely to delay the adoption of abatement policies as found in previous studies, with respect to the standard CBA; however (ii) the possibility of climate catastrophes accelerates the implementation of these policies as their net discounted benefits increase significantly.

In this paper, we investigate the optimal timing for deep geological disposal of nuclear waste. Our model is based on the real options approach to investment under uncertainty. In this context, the problem is similar to the optimal exercise policy for a perpetual American spread option. The potential usefulness of such a model for actual decision-making on a sensitive issue is illustrated by some numerical simulations.

Using the insights of current research in corporate finance and financial institutions, the authors briefly present a consistent economic framework for looking at insurance. Shareholders of insurance companies provide risk capital that is invested in financial assets and therefore earns the market return of the assets it is invested in. However, due to the legal and fiscal environment insurance companies are in, they have a competitive disadvantage at investing, and this gives rise to frictional capital costs. The core competence of insurers is in managing the size of these frictional capital costs. Insurers must ensure that they can sell insurance for a price in excess of what they need to produce the cover they sell and compensate the incurred frictional costs on risk capital. It is through the ability to do so that insurers create shareholder value.

Obra que surge de la necesidad de contar con una referencia de fácil acceso a uno de los instrumentos de cobertura de riesgo cambiario más eficientes: la opción sobre la divisa. Esta versión, publicada originalmente en francés, ha sido actualizada y adaptada al caso latinoamericano, en particular al mexicano. El libro expone gradualmente, yendo de lo simple a lo complicado, las herramientas relacionadas con el riesgo cambiario, expuestas a manera de hacerlas más accesibles al lector, quien además podrá remitirse directamente a los anexos que contienen los aspectos técnicos y los métodos de valuación de las opciones más recientes.

The conflict between shareholders and bondholders in a levered firm over the choice of the risk level for firm assets is well-known. The original contingent claims approach to this issue had the firm reaching a critical point at the bond maturity date, similar to what happens at expiration of an option. In that model, equity is shown to be like a call option on the value of the firm. But the reality is that firms are continuously monitored by investors, customers and employees, and may potentially experience financial distress if the value of its assets Falls too low at any point in time. In this article, Chesney and Gibson present an alternative contingent claims analysis, in which equity is modeled as a down and out call, with an outstrike equal to the asset level that would precipitate distress. In this revised framework, they are able to study how the use of convertible debt, or debt with attached warrants, in place of straight debt affects the problem of volatility choice, and may perhaps eliminate the conflict of interest entirely.

The recent flows of immigrants to many countries has been categorized by both legal/illegal migrants. Such migration flows have occurred despite the presence of domestic unemployment of various categories of labour. It has also been observed that migration has lowered the reward of unskilled workers. These problems are analysed on the basis of two alternative models: (i) where skilled workers and (ii) where unskilled workers are unemployed. It is shown that migration may raise both skilled/unskilled employment and welfare under plausible factor intensity conditions. More importantly, illegal migration may help in lowering the relative price of the non-traded good while the impact of migration on structural adjustment is ambiguous.

In this study we re-examine the pricing of equity and the risk incentives of shareholders in levered firms. We derive a down-and-out call equity valuation model which rests on the assumption that shareholders choose the optimal investment and asset returns' volatility as a function of current leverage. Contrarily to the Black and Scholes framework where, irrespective of the firm's leverage, they would always select infinite volatility projects, here the more deep out-of-the-money the shareholders' claim, the greater their incentives to select riskier investment projects. The model is thus consistent with and quantifies the asset substitution problem previously acknowledged by the agency literature.

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This paper sets up a model for analysing the problem of rational exit where the stopping time itself is part of the integration problem. The model development is for the case of smoking. Smoking produces pleasure, pain and addiction. Our model captures all these elements and using Brownian notion and continuous martingales establishes that “quit smoking” campaigns require a two pronged attack: educational and medical. It develops a new technique which can be applied to other stopping problems where stopping time itself is part of the integration problem.

This article addresses some of the valuation problems, in the Black and Scholes setting of a geometric Brownian motion for the underlying asset dynamics, for options whose pay-off is related to the terminal price of the stock and an arithmetic average of fixing and/or involves stopping times related to excursions. In all cases, we are able to provide at least the Laplace transform in time of the option price under a form whose complexity varies with the number of exotic features. We emphasize that we do not give closed form formulas for the general case, but we aim to develop a methodology which may be used in many cases.

In this paper we study a new kind of option, called hereinafter a Parisian barrier option. This option is the following variant of the so-called barrier option: a down-and-out barrier option becomes worthless as soon as a barrier is reached, whereas a down-and-out Parisian barrier option is lost by the owner if the underlying asset reaches a prespecified level and remains constantly below this level for a time interval longer than a fixed number, called the window. Properties of durations of Brownian excursions play an essential role. We also study another kind of option, called here a cumulative Parisian option, which becomes worthless if the total time spent below a certain level is too long.

There are basic misunderstandings on derivative markets. Some professionals believe that they are a kind of casinos and have no utility for the investors. This work looks at the effects of options introduction in the Brazilian market, seeking for another benefit for this introduction: changes in the stocks risk leveI. Our results are the same found in the US and other markets: the options introduction reduces the stocks volatility. We also found that there is a slight indication that the volatility becames more stochastic with this alternative.