BUYING VERSUS HIRING—AN INDIRECT EVOLUTIONARY APPROACH

On a symmetric homogeneous oligopoly market with stochastic demand, firms can either hire employees or buy their labor input on a competitive labor market. Whereas the wage of hired labor does not depend on the realization of stochastic demand, the price of ‘bought’ labor reacts positively to product demand. We derive the equilibrium price vector to define an evolutionary process, assuming that the number of hiring firms increases when they earn more than buying firms. We then derive and discuss the stationary distribution of this stochastic adaptation process.     

EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL‐STOCHASTIC VOLATILITY MODELS

We consider an asset whose risk‐neutral dynamics are described by a general class of local‐stochastic volatility models and derive a family of asymptotic expansions for European‐style option prices and implied volatilities. We also establish rigorous error estimates for these quantities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under four different model dynamics: constant elasticity of variance local volatility, Heston stochastic volatility, three‐halves stochastic volatility, and SABR local‐stochastic volatility.     

The Effects of Economic Integration and Political Instability in Central America

We use stochastic frontier analysis to study the effects of political instability events and economic integration on technical efficiency. A set of industries in Central America are analyzed during a period of perceived lack of regional economic integration (1980s) and a period of renewed economic integration (early 1990s). Results show that economic integration has had a negative effect on technical efficiency during this period. The effect from political instability depends on the type of event, both at the industry and national level.     

Mean‐field games with differing beliefs for algorithmic trading

Even when confronted with the same data, agents often disagree on a model of the real world. Here, we address the question of how interacting heterogeneous agents, who disagree on what model the real world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for the permanent impact they have on prices. This leads to a large stochastic game, where each agents performance criteria are computed under a different probability measure. We analyze the mean‐field game (MFG) limit of the stochastic game and show that the Nash equilibrium is given by the solution to a nonstandard vector‐valued forward–backward stochastic differential equation. Under some mild assumptions, we construct the solution in terms of expectations of the filtered states. Furthermore, we prove that the MFG strategy forms an ε‐Nash equilibrium for the finite player game. Finally, we present a least square Monte Carlo based algorithm for computing the equilibria and show through simulations that increasing disagreement may increase price volatility and trading activity.     

Hedging and Portfolio Optimization in Financial Markets with a Large Trader

We introduce a general continuous-time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter-dependent semimartingales, and its mathematical analysis relies on the nonlinear integration theory of such semimartingale families. The Itô–Wentzell formula is used to prove absence of arbitrage for the large investor, and, using approximation results for stochastic integrals, we characterize the set of approximately attainable claims. We furthermore show how to compute superreplication prices and discuss the large investor's utility maximization problem.     

Model-free portfolio theory: A rough path approach

Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on Föllmer integration. Without the assumption of any underlying probabilistic model, we prove a pathwise formula for the relative wealth process, which reduces in the special case of functionally generated portfolios to a pathwise version of the so-called master formula of classical SPT. We show that the appropriately scaled asymptotic growth rate of a far reaching generalization of Cover's universal portfolio based on controlled paths coincides with that of the best retrospectively chosen portfolio within this class. We provide several novel results concerning rough integration, and highlight the advantages of the rough path approach by showing that (nonfunctionally generated) log-optimal portfolios in an ergodic Itô diffusion setting have the same asymptotic growth rate as Cover's universal portfolio and the best retrospectively chosen one.     

An explicitly solvable multi‐scale stochastic volatility model: Option pricing and calibration problems

We introduce an explicitly solvable multiscale stochastic volatility model that generalizes the Heston model. The model describes the dynamics of an asset price and of its two stochastic variances using a system of three Ito stochastic differential equations. The two stochastic variances vary on two distinct time scales and can be regarded as auxiliary variables introduced to model the dynamics of the asset price. Under some assumptions, the transition probability density function of the stochastic process solution of the model is represented as a one‐dimensional integral of an explicitly known integrand. In this sense the model is explicitly solvable. We consider the risk‐neutral measure associated with the proposed multiscale stochastic volatility model and derive formulae to price European vanilla options (call and put) in the multiscale stochastic volatility model considered. We use the thus‐obtained option price formulae to study the calibration problem, that is to study the values of the model parameters, the correlation coefficients of the Wiener processes defining the model, and the initial stochastic variances implied by the “observed” option prices using both synthetic and real data. In the analysis of real data, we use the S&P 500 index and to the prices of the corresponding options in the year 2005. The web site http://www.econ.univpm.it/recchioni/finance/w7 contains some auxiliary material including some animations that helps the understanding of this article. A more general reference to the work of the authors and their coauthors in mathematical finance is the web site http://www.econ.univpm.it/recchioni/finance . © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:862–893, 2009     

Price‐level co‐movements within currency unions: An alternative integration metric

This paper analyses currency union integration by testing whether price levels in member countries possess a common stochastic trend. The trace statistic test for cointegration proposed by (Johansen, 1995) demonstrates the presence of such a trend for most unions. A disaggregated analysis identifies a common stochastic trend for several though fewer than half of country pairs within a union. Some unions such as the Eurozone have small shares of cointegrated country pairs. Yet, the share of cointegrated country pairs is large relative to countries outside currency unions. Comparison to a control group (country pairs where one country belongs to a given union and the other country does not) indicates that the cointegration found within a currency union is a union‐specific trait and not a feature of the individual countries within the union. These results provide an alternative metric to intraunion trade for gauging the extent of currency union integration.     

The Gravity Model and Trade Efficiency: A Stochastic Frontier Analysis of Eastern European Countries' Potential Trade

The opening up process of the eastern European countries is characterised by an increasing degree of trade integration with their Western neighbouring countries. Typically, the degree of East–West trade integration is assessed by comparing actual trade volumes with potential trade volumes projected from the gravity model parameters estimated for a group of countries that best represent normal trade relations. This approach, however, does not compare trade levels against a maximum level of trade feasible for the group of eastern European countries. This paper using a stochastic frontier specification of the gravity model is able to identify the efficiency of trade integration relative to maximum potential levels. The findings, based on a panel data set of bilateral exports from 17 Western European countries to the 10 new member states over the 1994–2007 period, indicate a high degree of East–West trade integration close to two‐thirds of frontier estimates, suggesting a low degree of trade resistances.     

International trade and macroeconomic dynamics with labor market frictions

This paper studies how labor market frictions affect the consequences of trade integration in a two-country dynamic stochastic general equilibrium model with heterogeneous firms and endogenous producer entry. Two main results emerge. First, trade integration is beneficial for welfare by inducing higher productivity, but unemployment can temporarily rise during the transitional adjustment. Labor market rigidities reduce gains from trade, even though they can mitigate short-run employment losses. Second, consistent with the data, the model predicts that stronger trade linkages lead to increased business cycle synchronization. The strength of this effect, however, depends on the labor market characteristics of the integrating partners.     

Endogenous discounting, the world saving glut and the U.S. current account

We study the evolution of the U.S. current account in a two-country dynamic stochastic endowment model in which a single non-state contingent bond is the only internationally traded asset. The paper focuses on the world ‘saving glut’ as the primary cause of continual deterioration in the current account and departs from the standard framework by introducing a three-parameter model of the subjective discount factor that depends on societal (per capita) variables that are external to household choices. When agents in the model are presented with U.S. and rest-of-world endowment data as the realization of the exogenous state vector, endogenously driven short-run international differences in subjective discounting that display increasing relative U.S. impatience create saving and current account imbalances that matches patterns observed in the data.     

The RMB Debate: Empirical Analysis on the Effects of Exchange Rate Shocks in China and Japan

For a better understanding of the ongoing debates on the RMB, this paper investigates the effects of exchange rate shocks on output and the current account for China and Japan. We use structural vector auto‐regression models and find that yen appreciation reduces current account surpluses while having no strong effect on output in Japan. RMB appreciation, on the other hand, has an insignificant effect on the current account, although it tends to reduce output in China. For China, dollar pricing with vertical trade integration seems responsible for the insignificant effect on the current account.     

THE STOCHASTIC VOLATILITY MODEL OF BARNDORFF‐NIELSEN AND SHEPHARD IN COMMODITY MARKETS

We consider the non‐Gaussian stochastic volatility model of Barndorff‐Nielsen and Shephard for the exponential mean‐reversion model of Schwartz proposed for commodity spot prices. We analyze the properties of the stochastic dynamics, and show in particular that the log‐spot prices possess a stationary distribution defined as a normal variance‐mixture model. Furthermore, the stochastic volatility model allows for explicit forward prices, which may produce a hump structure inherited from the mean‐reversion of the stochastic volatility. Although the spot price dynamics has continuous paths, the forward prices will have a jump dynamics, where jumps occur according to changes in the volatility process. We compare with the popular Heston stochastic volatility dynamics, and show that the Barndorff‐Nielsen and Shephard model provides a more flexible framework in describing commodity spot prices. An empirical example on UK spot data is included.     

Do deeper regional trade agreements enhance international technology spillovers?

We examine whether regional trade agreements (RTAs) enhance international technology spillovers using a panel of patent citation data for 114 countries/regions for the period 1991–2007. We use patent citations as a proxy for technology spillovers. The focus of this study is on whether the depth of regional integration matters for technology spillovers among member countries/regions of RTAs. The depth of integration is measured by the extent to which an RTA includes legal obligations outside the current mandate of the World Trade Organization. We find that the depth of integration actually influences technology spillovers and that a deeper integration in a broad sense has a greater impact on technology spillovers than do technology‐related provisions.     

The Effect of 2008 Crisis on the Volatility Spillovers among Six Major Markets

The scope of this paper is to determine whether global stock markets function differently under conditions of economic crisis by measuring volatility spillovers between six major markets, namely the US, the UK, Germany, Spain, Turkey, and Greece. We examine the volatility spillover effects of the 2008 US financial crisis to these six major markets using daily stock returns from January 2003 to December 2014, before, during, and after the 2008 financial crisis. We combine the Diebold and Yilmaz methodology with the stochastic volatility model of Taylor implemented through the sequential Efficient Importance Sampling method of Richard and Zhang to obtain variance decompositions derived from an estimated vector autoregressive model. The empirical findings suggest that stock markets tend to show increased volatility spillovers during the crisis period, thus resulting in lesser diversification benefits for investors.     

Conic martingales from stochastic integrals

In this paper, we introduce the concept of conic martingales. This class refers to stochastic processes that have the martingale property but that evolve within given (possibly time‐dependent) boundaries. We first review some results about the martingale property of solution to driftless stochastic differential equations. We then provide a simple way to construct and handle such processes. Specific attention is paid to martingales in [0, 1]. One of these martingales proves to be analytically tractable. It is shown that up to shifting and rescaling constants, it is the only martingale (with the trivial constant, Brownian motion, and geometric Brownian motion) having a separable diffusion coefficient and that can be obtained via a time‐homogeneous mapping of Gaussian diffusions. The approach is exemplified by modeling stochastic conditional survival probabilities in the univariate and bivariate cases.     

Small‐cost asymptotics for long‐term growth rates in incomplete markets

This paper provides a rigorous asymptotic analysis of long‐term growth rates under both proportional and Morton–Pliska transaction costs. We consider a general incomplete financial market with an unspanned Markov factor process that includes the Heston stochastic volatility model and the Kim–Omberg stochastic excess return model as special cases. Using a dynamic programming approach, we determine the leading‐order expansions of long‐term growth rates and explicitly construct strategies that are optimal at the leading order. We further analyze the asymptotic performance of Morton–Pliska strategies in settings with proportional transaction costs. We find that the performance of the optimal Morton–Pliska strategy is the same as that of the optimal one with costs increased by a factor of . Finally, we demonstrate that our strategies are in fact pathwise optimal, in the sense that they maximize the long‐run growth rate path by path.     

A UNIVERSAL OPTIMAL CONSUMPTION RATE FOR AN INSIDER

We consider a cash flow   X ^{( c )} ( t )  modeled by the stochastic equation where B (·) and     are a Brownian motion and a Poissonian random measure, respectively, and   c ( t ) ≥ 0  is the consumption/dividend rate. No assumptions are made on adaptedness of the coefficients  μ, σ, θ  , and c , and the (possibly anticipating) integrals are interpreted in the forward integral sense. We solve the problem to find the consumption rate c (·), which maximizes the expected discounted utility given by Here  δ( t ) ≥ 0  is a given measurable stochastic process representing a discounting exponent and τ is a random time with values in (0, ∞), representing a terminal/default time, while  γ≥ 0  is a known constant.     

EFFICIENT PRICING OF BARRIER OPTIONS AND CREDIT DEFAULT SWAPS IN LÉVY MODELS WITH STOCHASTIC INTEREST RATE

Recently, advantages of conformal deformations of the contours of integration in pricing formulas for European options have been demonstrated in the context of wide classes of Lévy models, the Heston model, and other affine models. Similar deformations were used in one‐factor Lévy models to price options with barrier and lookback features and credit default swaps (CDSs). In the present paper, we generalize this approach to models, where the dynamics of the assets is modeled as , where X is a Lévy process, and the interest rate is stochastic. Assuming that X and r are independent, and , the infinitesimal generator of the pricing semigroup in the model for the short rate, satisfies weak regularity conditions, which hold for popular models of the short rate, we develop a variation of the pricing procedure for Lévy models which is almost as fast as in the case of the constant interest rate. Numerical examples show that about 0.15 second suffices to calculate prices of 8 options of same maturity in a two‐factor model with the error tolerance and less; in a three‐factor model, accuracy of order 0.001–0.005 is achieved in about 0.2 second. Similar results are obtained for quanto CDS, where an additional stochastic factor is the exchange rate. We suggest a class of Lévy models with the stochastic interest rate driven by 1–3 factors, which allows for fast calculations. This class can satisfy the current regulatory requirements for banks mandating sufficiently sophisticated credit risk models.     

Bounds on European Option Prices under Stochastic Volatility

In this paper we consider the range of prices consistent with no arbitrage for European options in a general stochastic volatility model. We give conditions under which the infimum and the supremum of the possible option prices are equal to the intrinsic value of the option and to the current price of the stock, respectively, and show that these conditions are satisfied in most of the stochastic volatility models from the financial literature. We also discuss properties of Black–Scholes hedging strategies in stochastic volatility models where the volatility is bounded.