Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

Monetary policy and exchange rate volatility in a small open economy

We lay out a small open economy version of the Calvo sticky price model, and show how the equilibrium dynamics can be reduced to simple representation in domestic inflation and the output gap. We use the resulting framework to analyze the macroeconomic implications of three alternative rule-based policy regimes for the small open economy: domestic inflation and CPI-based Taylor rules, and an exchange rate peg. We show that a key difference amongthese regimes lies in the relative amount of exchange rate volatility that they entail. We also discuss a special case for which domestic inflation targeting constitutes the optimal policy, and where a simple second order approximation to the utility of the representative consumer can be derived and used to evaluate the welfare losses associated with the suboptimal rules.

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

Financial stress transmission in EMU sovereign bond market volatility: a connectedness analysis

This paper measures the connectedness in EMU sovereign market volatility between April 1999 and January 2014, in order to monitor stress transmission and to identify episodes of intensive spillovers from one country to the others. To this end, we first perform a static and dynamic analysis to measure the total volatility connectedness in the entire period (the system-wide approach) using a framework recently proposed by Diebold and Yılmaz (2014). Second, we make use of a dynamic analysis to evaluate the net directional connectedness for each country and apply panel model techniques to investigate its determinants. Finally, to gain further insights, we examine the timevarying behaviour of net pair-wise directional connectedness at different stages of the recent sovereign debt crisis.

Volatility spillovers in EMU sovereign bond markets

We analyse volatility spillovers in EMU sovereign bond markets. First, we examine the unconditional patterns during the full sample (April 1999-January 2014) using a measure recently proposed by Diebold and Yılmaz (2012). Second, we make use of a dynamic analysis to evaluate net directional volatility spillovers for each of the eleven countries under study, and to determine whether core and peripheral markets present differences. Finally, we apply a panel analysis to empirically investigate the determinants of net directional spillovers of this kind.

Security prices and market transparency: the role of prior information

This paper analyzes the role of traders' priors (proper versus improper) on the implications of market transparency by comparing a pre-trade transparent market with an opaque market in a set-up based on Madhavan (1996). We show that prices may be more informative in the opaque market, regardless of how priors are modelled. In contrast, the comparison of market liquidity and volatility in the two market structures are affected by prior specification. Key words: Market microstructure, Transparency, Prior information

How tight should one's hands be tied? Fear of floating and credibility of exchange rate regimes

This paper analyzes the linkages between the credibility of a target zone regime, the volatility of the exchange rate, and the width of the band where the exchange rate is allowed to fluctuate. These three concepts should be related since the band width induces a trade-off between credibility and volatility. Narrower bands should give less scope for the exchange rate to fluctuate but may make agents perceive a larger probability of realignment which by itself should increase the volatility of the exchange rate. We build a model where this trade-off is made explicit. The model is used to understand the reduction in volatility experienced by most EMS countries after their target zones were widened on August 1993. As a natural extension, the model also rationalizes the existence of non-official, implicit target zones (or fear of floating), suggested by some authors.

Auctions for government securities: a laboratory comparison of uniform, discriminatory and spanish designs

The Bank of Spain uses a unique auction format to sell government bonds, which can be seen as a hybrid of a uniform and a discriminatory auction. For winning bids above the average winning bid, buyers are charged the average winning bid, otherwise they pay their respective bids. We report on an experiment that compares this auction format to the discriminatory format, used in most other countries, and to the uniform format. Our design is based on a common value model with multi-unit supply and two-unit demand. The results show significantly higher revenue with the Spanish and the uniform formats than with the discriminatory one, while volatility of prices over time is significantly lower in the discriminatory format than in the Spanish and uniform cases. Actual price dispersion is significantly larger in the discriminatory than in the Spanish. Our data also exhibit the use of bid-spreading strategies in all three designs.

On the choice of an exchange rate regime: target zones revisited

From the classical gold standard up to the current ERM2 arrangement of the European Union, target zones have been a widely used exchange regime in contemporary history. This paper presents a benchmark model that rationalizes the choice of target zones over the rest of regimes: the fixed rate, the free float and the managed float. It is shown that the monetary authority may gain efficiency by reducing volatility of both the exchange rate and the interest rate at the same time. Furthermore, the model is consistent with some known stylized facts in the empirical literature that previous models were not able to produce, namely, the positive relation between the exchange rate and the interest rate differential, the degree of non-linearity of the function linking the exchage rate to fundamentals and the shape of the exchange rate stochastic distribution.

The relevance of post-match LTC: why has the Spanish labor market become as volatile as the US one?

We present a Search and Matching model with heterogeneous workers (entrants and incumbents) that replicates the stylized facts characterizing the US and the Spanish labor markets. Under this benchmark, we find the Post-Match Labor Turnover Costs (PMLTC) to be the centerpiece to explain why the Spanish labor market is as volatile as the US one. The two driving forces governing this volatility are the gaps between entrants and incumbents in terms of separation costs and productivity. We use the model to analyze the cyclical implications of changes in labor market institutions affecting these two gaps. The scenario with a low degree of workers’ heterogeneity illustrates its suitability to understand why the Spanish labor market has become as volatile as the US one.

Codes of best practice in competitive markets for managers

We study firms' corporate governance in environments where possibly heterogeneous shareholders compete for possibly heterogeneous managers. A firm, formed by a shareholder and a manager, can sign either an incentive contract or a contract including a Code of Best Practice. A Code allows for a better manager's control but makes manager's decisions hard to react when market conditions change. It tends to be adopted in markets with low volatility and in low-competitive environments. The firms with the best projects tend to adopt the Code when managers are not too heterogeneous while the best managers tend to be hired through incentive contracts when the projects are similar. Although the matching between shareholders and managers is often positively assortative, the shareholders with the best projects might be willing to renounce to hire the best managers, signing contracts including Codes with lower-ability managers.

Understanding sources of the change in international business cycles

Macroeconomic activity has become less volatile over the past three decades in most G7 economies. Current literature focuses on the characterization of the volatility reduction and explanations for this so called "moderation" in each G7 economy separately. In opposed to individual country analysis and individual variable analysis, this paper focuses on common characteristics of the reduction and common explanations for the moderation in G7 countries. In particular, we study three explanations: structural changes in the economy, changes in common international shocks and changes in domestic shocks. We study these explanations in a unified model structure. To this end, we propose a Bayesian factor structural vector autoregressive model. Using the proposed model, we investigate whether we can find common explanations for all G7 economies when information is pooled from multiple domestic and international sources. Our empirical analysis suggests that volatility reductions can largely be attributed to the decline in the magnitudes of the shocks in most G7 countries while only for the U.K., the U.S. and Italy they can partially be attributed to structural changes in the economy. Analyzing the components of the volatility, we also find that domestic shocks rather than common international shocks can account for a large part of the volatility reduction in most of the G7 countries. Finally, we find that after mid-1980s the structure of the economy changes substantially in five of the G7 countries: Germany, Italy, Japan, the U.K. and the U.S..

A nonlinear threshold model for the dependence of extremes of stationary sequences

One of the main implications of the efficient market hypothesis (EMH) is that expected future returns on financial assets are not predictable if investors are risk neutral. In this paper we argue that financial time series offer more information than that this hypothesis seems to supply. In particular we postulate that runs of very large returns can be predictable for small time periods. In order to prove this we propose a TAR(3,1)-GARCH(1,1) model that is able to describe two different types of extreme events: a first type generated by large uncertainty regimes where runs of extremes are not predictable and a second type where extremes come from isolated dread/joy events. This model is new in the literature in nonlinear processes. Its novelty resides on two features of the model that make it different from previous TAR methodologies. The regimes are motivated by the occurrence of extreme values and the threshold variable is defined by the shock affecting the process in the preceding period. In this way this model is able to uncover dependence and clustering of extremes in high as well as in low volatility periods. This model is tested with data from General Motors stocks prices corresponding to two crises that had a substantial impact in financial markets worldwide; the Black Monday of October 1987 and September 11th, 2001. By analyzing the periods around these crises we find evidence of statistical significance of our model and thereby of predictability of extremes for September 11th but not for Black Monday. These findings support the hypotheses of a big negative event producing runs of negative returns in the first case, and of the burst of a worldwide stock market bubble in the second example. JEL classification: C12; C15; C22; C51 Keywords and Phrases: asymmetries, crises, extreme values, hypothesis testing, leverage effect, nonlinearities, threshold models

Market effects of foreign exchange coordinated intervention

In this article we develop a theoretical microstructure model of coordinated central bank intervention based on asymmetric information. We study the economic implications of coordination on some measures of market quality and show that the model predicts higher volatility and more significant exchange rate changes when central banks coordinate compared to when they intervene unilaterally. Both these predictions are in line with empirical evidence. Keywords: coordinated foreign exchange intervention, market microstructure. JEL Classification: D82, E58, F31, G14

In Search of a theory of debt management

A growing literature integrates theories of debt management into models of optimal fiscal policy. One promising theory argues that the composition of government debt should be chosen so that fluctuations in the market value of debt offset changes in expected future deficits. This complete market approach to debt management is valid even when the government only issues non-contingent bonds. A number of authors conclude from this approach that governments should issue long term debt and invest in short term assets. We argue that the conclusions of this approach are too fragile to serve as a basis for policy recommendations. This is because bonds at different maturities have highly correlated returns, causing the determination of the optimal portfolio to be ill-conditioned. To make this point concrete we examine the implications of this approach to debt management in various models, both analytically and using numerical methods calibrated to the US economy. We find the complete market approach recommends asset positions which are huge multiples of GDP. Introducing persistent shocks or capital accumulation only worsens this problem. Increasing the volatility of interest rates through habits partly reduces the size of these simulations we find no presumption that governments should issue long term debt ? policy recommendations can be easily reversed through small perturbations in the specification of shocks or small variations in the maturity of bonds issued. We further extend the literature by removing the assumption that governments every period costlessly repurchase all outstanding debt. This exacerbates the size of the required positions, worsens their volatility and in some cases produces instability in debt holdings. We conclude that it is very difficult to insulate fiscal policy from shocks by using the complete markets approach to debt management. Given the limited variability of the yield curve using maturities is a poor way to substitute for state contingent debt. The result is the positions recommended by this approach conflict with a number of features that we believe are important in making bond markets incomplete e.g allowing for transaction costs, liquidity effects, etc.. Until these features are all fully incorporated we remain in search of a theory of debt management capable of providing robust policy insights.