Step Options

Motivated by risk management problems with barrier options, we propose a flexible modification of the standard knock‐out and knock‐in provisions and introduce a family of path‐dependent options: step options . They are parametrized by a finite knock‐out (knock‐in) rate , ρ. For a down‐and‐out step option, its payoff at expiration is defined as the payoff of an otherwise identical vanilla option discounted by the knock‐out factor exp(-ρτ_B^‐) or max(1‐ρτ^-B,0), where &\tau;_B^‐ is the total time during the contract life that the underlying price was lower than a prespecified barrier level ( occupation time ). We derive closed‐form pricing formulas for step options with any knock‐out rate in the range $[0,∞). For any finite knock‐out rate both the step option's value and delta are continuous functions of the underlying price at the barrier. As a result, they can be continuously hedged by trading the underlying asset and borrowing. Their risk management properties make step options attractive "no‐regrets" alternatives to standard barrier options. As a by‐product, we derive a dynamic almost‐replicating trading strategy for standard barrier options by considering a replicating strategy for a step option with high but finite knock‐out rate. Finally, a general class of derivatives contingent on occupation times is considered and closed‐form pricing formulas are derived.     

Changing economic mechanisms: A model of the transition from budget regulation to the competitive market

Summary In the framework of dynamic equilibrium theory we propose a model of gradual transition from an Economy with centralized budgets regulation to a Market Economy (with self-financing). It is assumed that information about possible change of the economic mechanism affects essentially the behavior of agents. The duration of the transition period is regarded as a random variable. We study conditions when such a transition allows firms to adapt their plans to future markets and guarantees the existence of equilibrium paths. We also discuss the case of Shock Therapy (instantaneous transition) which may cause bankruptcy, jumps in prices and deficits.This work is supported by Russian Foundation of Basic Researches, grant 93-06-10356     

A jump to default extended CEV model: an application of Bessel processes

We develop a flexible and analytically tractable framework which unifies the valuation of corporate liabilities, credit derivatives, and equity derivatives. We assume that the stock price follows a diffusion, punctuated by a possible jump to zero (default). To capture the positive link between default and equity volatility, we assume that the hazard rate of default is an increasing affine function of the instantaneous variance of returns on the underlying stock. To capture the negative link between volatility and stock price, we assume a constant elasticity of variance (CEV) specification for the instantaneous stock volatility prior to default. We show that deterministic changes of time and scale reduce our stock price process to a standard Bessel process with killing. This reduction permits the development of completely explicit closed form solutions for risk-neutral survival probabilities, CDS spreads, corporate bond values, and European-style equity options. Furthermore, our valuation model is sufficiently flexible so that it can be calibrated to exactly match arbitrarily given term structures of CDS spreads, interest rates, dividend yields, and at-the-money implied volatilities.     

What model for entry in first-price auctions? A nonparametric approach

We develop a selective entry model for first-price auctions that nests two polar models often estimated in the empirical literature on auctions, Levin and Smith (1994), and Samuelson (1985). The selective entry model features a pro-competitive selection effect. The selection effect is shown to be nonparametrically identifiable, and a nonparametric test for its presence is proposed. This test can be used to discriminate between the two polar models.     

Economic,structural and socio‐psychological determinants of protests in Russia during 2011–2012

This empirical analysis is based on the latent variable framework to identify key determinants of protests in Russia during 2011–2012. We derive logistic regressions from the revolution constraints based on economic (the political Kuznets Curve) and socio‐psychological (grievance) theories of protest. Our findings suggest a positive linear relationship between income and income inequality, contradicting the Kuznets curve. Our estimations show that inequality, share of the poor, the relation of the governor's family income to the average family income, distance to Moscow and accumulated human capital increase the risk of protest, whereas transfers and subsidies decrease these risks.     

Is There Room for an Independent Trade Unionism in Russia? Trade Unionism in the Russian Aviation Industry

On the basis of a detailed study of two 'independent' unions, representing pilots and air traffic controllers, this paper argues that there are very limited prospects for independent trade unionism in Russia at present. The air traffic controllers' union has adopted a resolutely independent and militant strategy of pursuing the sectional interests of its members, which has brought it into conflict with management, other unions and the government. The pilots' union, by contrast, has sought to consolidate the position of its members as a labour aristocracy, collaborating closely with management to secure its privileged position. The success of the pilots contrasts starkly with the heavy defeat suffered by the air traffic controllers following their strikes in August and December 1992, indicating the barriers that face the attempt to create trade unions independent of management in Russia.     

TIME‐CHANGED ORNSTEIN–UHLENBECK PROCESSES AND THEIR APPLICATIONS IN COMMODITY DERIVATIVE MODELS

This paper studies subordinate Ornstein–Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy subordinators. We construct their sample path decomposition, show that they possess mean‐reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigroups in terms of Hermite expansions. As an application, we propose a new class of commodity models with mean‐reverting jumps based on subordinate OU processes. Further time changing by the integral of a Cox–Ingersoll–Ross process plus a deterministic function of time, we induce stochastic volatility and time inhomogeneity, such as seasonality, in the models. We obtain analytical solutions for commodity futures options in terms of Hermite expansions. The models are consistent with the initial futures curve, exhibit Samuelson's maturity effect, and are flexible enough to capture a variety of implied volatility smile patterns observed in commodities futures options.     

Optimal comparison of misspecified moment restriction models under a chosen measure of fit

Suppose that the econometrician is interested in comparing two misspecified moment restriction models, where the comparison is performed in terms of some chosen measure of fit. This paper is concerned with describing an optimal test of the Vuong (1989) and Rivers and Vuong (2002) type null hypothesis that the two models are equivalent under the given measure of fit (the ranking may vary for different measures). We adopt the generalized Neyman–Pearson optimality criterion, which focuses on the decay rates of the type I and II error probabilities under fixed non-local alternatives, and derive an optimal but practically infeasible test. Then, as an illustration, by considering the model comparison hypothesis defined by the weighted Euclidean norm of moment restrictions, we propose a feasible approximate test statistic to the optimal one and study its asymptotic properties. Local power properties, one-sided test, and comparison under the generalized empirical likelihood-based measure of fit are also investigated. A simulation study illustrates that our approximate test is more powerful than the Rivers–Vuong test.