Sandro Claudio Lera

Quantitative Modelling of the EUR/CHF Exchange Rate during the Target Zone Regime of September 2011 to January 2015

Krugman(1991)’s target zone model has become the reference of a large part of this literature. Despite its simplicity and elegance, empirical evidence has been lacking. Deriving from Krugman’s model analytical expressions for the conditional volatility and density distribution close to the target zone limit, we present clear and direct evidence that the bounded EUR/CHF exchange rate between September 2011 and January 2015 was quantitatively well described by Krugman’s model. Krugman’s target zone model holds after all, but apparently only under extreme and sustained pressure that pushes continuously the exchange rate very close to the boundary of the target zone.Krugman (1991)s target zone model for exchange rate dynamics has become the reference of a large part of this literature. Despite its simplicity and elegance, empirical evidence has been lacking, not least because it is difficult to capture the predicted non-linear relationship between the observable exchange rate and the non-observable fundamental value. This is why we propose a different approach. By inverting locally the relation between exchange rate and fundamental value, we derive analytical expressions for the conditional volatility and the probability density as a function of the exchange rate. This allows us to examine Krugmans prediction directly from historical data, and, furthermore, enables us to test the smooth pasting condition, which is intimately related to the no-arbitrage condition. Concretely, we study the performance of the euro/Swiss franc exchange rate in the extraordinary period from September 6, 2011 to January 15, 2015, when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. We show that the data are well explained by the theory and conclude that Krugmans target zone model holds after all, but apparently only under extreme and sustained pressure that pushes continuously the exchange rate very close to the boundary of the target zone.

An Explicit Mapping of Currency Target Zone Models to Option Prices

Currency target zones have been under scrutiny for the past three decades, which led to the development of two broad classes of quantitative models: Phenomenological ones that explicitly take into consideration the market’s perception of the bounded exchange rate, and more mechanical ones that rely on put and call options. Until now, the two models have only been compared qualitatively. Here, we derive, for the first time, a quantitative link between these two approaches. Specifically, we show how the former approach has to be generalized in order to recover the second one. This mapping lets us relate the phenomenological parameter of the first approach to economically well-known quantities.

Quantification of the evolution of firm size distributions due to mergers and acquisitions

The distribution of firm sizes is known to be heavy tailed. In order to account for this stylized fact, previous economic models have focused mainly on growth through investments in a company’s own operations (internal growth). Thereby, the impact of mergers and acquisitions (M&A) on the firm size (external growth) is often not taken into consideration, notwithstanding its potential large impact. In this article, we make a first step into accounting for M&A. Specifically, we describe the effect of mergers and acquisitions on the firm size distribution in terms of an integro-differential equation. This equation is subsequently solved both analytically and numerically for various initial conditions, which allows us to account for different observations of previous empirical studies. In particular, it rationalises shortcomings of past work by quantifying that mergers and acquisitions develop a significant influence on the firm size distribution only over time scales much longer than a few decades. This explains why M&A has apparently little impact on the firm size distributions in existing data sets. Our approach is very flexible and can be extended to account for other sources of external growth, thus contributing towards a holistic understanding of the distribution of firm sizes.

Quantification of the Evolution of Firm Size Distributions Due to Mergers and Acquisitions

The distribution of firm sizes is known to be heavy tailed. In order to account for this stylized fact, previous studies have focused mainly on growth through investments in a company’s own operations (internal growth). Thereby, the impact of mergers and acquisitions (M&A) on the firm size (external growth) is often not taken into consideration, notwithstanding its potential large impact. In this article, we make a first step into accounting for M&A. Specifically, we describe the effect of mergers and acquisitions on the firm size distribution in terms of an integro-differential equation. This equation is subsequently solved both analytically and numerically for various initial conditions, which allows us to account for different observations of previous empirical studies. In particular, it rationalises shortcomings of past work by quantifying that, in order to observe a significant influence of mergers and acquisitions on the firm size distribution, more extensive datasets would have been required. Our approach is very flexible and can be extended to account for other sources of external growth, thus contributing towards a holistic understanding of the distribution of firm sizes.