Marc Chesney

Mathematical Methods for Financial Markets

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, Levy 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.

Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model

We use the modified Black-Scholes model and a random variance option pricing model to study prices of European currency options traded in Geneva. The options, which cannot be exercised early, include calls and puts on the dollar/Swiss franc exchange rate. In the empirical analysis, we examine the model fit and the biases with respect to the strike price, time to maturity, and volatility. There is some evidence of mispricing and there are small gains available by trading with the random variance model.

The Endogenous Price Dynamics of Emission Allowances and an Application to CO2 Option Pricing

Market mechanisms are increasingly being used as a tool for allocating somewhat scarce but unpriced rights and resources, and the European Emission Trading Scheme is an example. By means of dynamic optimization in the contest of firms covered by such environmental regulations, this paper generates endogenously the price dynamics of emission permits under asymmetric information, allowing inter-temporal banking and borrowing. In the market there are a finite number of firms and each firm’s pollution emission follows an exogenously given stochastic process. We prove the discounted permit price is a martingale with respect to the relevant filtration. The model is solved numerically. Finally, a closed-form pricing formula for European-style options is derived.

The impact of possible climate catastrophes on global warming policy

Abstract 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.

Long-term risk management of nuclear waste: a real options approach

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.

Reducing Asset Substitution with Warrant and Convertible Debt Issue

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.

American Parisian Options

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.

An Experimental Study on Real Option Strategies

We conduct a laboratory experiment to study whether people intuitively use real-option strategies in a dynamic investment setting. The participants were asked to play as an oil manager and make production decisions in response to a simulated mean-reverting oil price. Using cluster analysis, participants can be classified into four groups, which we label ‘mean-reverting’, ‘Brownian motion real-option’, ‘Brownian motion myopic real-option’, and ‘ambiguous’. We find two behavioral biases in the strategies of our participants: ignoring the mean-reverting process, and myopic behavior. Both lead to too frequent switches when compared with the theoretical benchmark. We also find that the last group behaved as if they have learned to incorporate the true underlying process into their decisions, and improved their decisions during the later stage.

Optimal Timing to Adopt an Environmental Policy in a Strategic Framework

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.

The Issue of Climate Change

According to the Intergovernmental Panel on Climate Change (IPCC) which aggregates international research efforts on climate change, global atmospheric concentrations of greenhouse gases (CO2, CH4 and N2O) have increased markedly as a results of human activities since 1750. As their concentrations in the atmosphere intensify, GHG act as a radiation trap that forces more energy to stay on surface and more heat to be produced, therefore causing global warming. According to the sensitivity projections of the IPCC, any commitment to limit the global average temperature increase within a +2 °C limit would force to stabilize CO2 concentration around 350–400 ppm. However, until damages are elicited and adaptation cost monetized, the urgency of taking measure against global warming remains for many elusive. This chapter will present the two clearest possible strategies to limit the causes of climate change and its impact, mitigation and adaptation strategies and details their respective strengths and weaknesses. We show that to be effective, an a optimal policy against climate changes and their impacts will have to combine both mitigation and adaptation. While adaptation are easier to implement, bear less uncertainties and can be privatized (partially avoiding free-riding effects), mitigation strategies are the only capable to reduce GHGs in the atmosphere in order to reestablish a viable long-term CO2 concentration.