Nonlinear dynamics in economic modelling

Decisions in Economics and Finance -     

Some reflections on past and future of nonlinear dynamics in economics and finance

This paper offers an overview of the literature on the economic and financial applications of theory of nonlinear dynamics, especially bifurcation theory. After a short introductory discussion of the first nonlinear dynamic models in social sciences and the economic relevance of the zoo of bifurcations and complicated dynamics that such models can generate, we present an overview of the literature on nonlinear dynamic models in the areas of underdevelopment, environmental poverty traps, the management of common goods, industrial organization and financial markets. The review of the literature is enriched by reflections and ideas for future research.     

A revised version of the Cathcart & El-Jahel model and its application to CDS market

Decisions in Economics and Finance - The paper considers the pricing of credit default swaps (CDSs) using a revised version of the credit risk model proposed in Cathcart and El-Jahel (2003)....     

Variable neighborhood search heuristic for nonconvex portfolio optimization

Abstract

In this article we consider a portfolio optimization problem under multiple real-world constraints, such as: cardinality constraints, tracking error, active share, and turnover. We propose a heuristic based on variable neighborhood search (VNS) that effectively addresses additional constraints that introduce non-convexities. In the VNS-based heuristic, several neighborhood structures are introduced and fast local search is implemented. We develop a VNS portfolio rebalancing framework (VNS-PRF) with two rebalance strategies. Data sets provided by a financial investment firm are used to evaluate the validity and reliability of the proposed VNS-PRF. Computational experiments and different portfolio performance measures indicate that our approach is able to obtain solutions with competitive quality and can be applied on large-scale data sets.     

Computing the survival probability in the Madan–Unal credit risk model: application to the CDS market

We obtain a quasi-analytical approximation of the survival probability in the credit risk model proposed in [Madan, D.B. and Unal, H., Pricing the risk of default. Rev. Deriv. Res., 1998, 2(2), 121–160]. Such a formula, which extensive numerical simulations reveal to be accurate and computationally fast, can also be employed for pricing credit default swaps (CDSs). Specifically, we derive a quasi-analytical approximate expression for CDS par spreads, and we use it to estimate the parameters of the model. The results obtained show a rather satisfactory agreement between theoretical and real market data.     

Hybrid dynamics of multi-species resource exploitation

Decisions in Economics and Finance - In this paper, we analyze a bio-economic model of exploitation of renewable commercial resources. To take into account the typically continuous-time modeling of...     

Competition and risk‐taking in investment banking

How does competition affect the investment banking business and the risks individual institutions are exposed to? Using a large sample of investment banks operating in seven developed economies over 1997–2014, we apply a panel VAR model to examine the relationships between competition and risk without assuming any a priori restrictions. Our main finding is that investment banks’ higher risk exposure, measured as a long‐term capital‐at‐risk and return volatility, was facilitated by greater competitive pressures for both boutique investment banks and full‐service investment banks. Overall, we find some evidence that more competition leads to more fragility before and during the recent financial crisis.     

Valuing investment projects under interest rate risk: empirical evidence from European firms

In this article, we perform an empirical investigation of the effect of the interest rate uncertainty on the valuation of investment projects. The analysis is carried out by employing a real option approach and by considering a set of firms that operate in various production sectors in the euro area. In particular, the revenues generated by the investment projects are modelled using a geometric Brownian motion, whereas the interest rate is specified as a stochastic process of Vasicek type. Moreover, using the volatility of the equity return as a proxy, the volatility of the revenues is calibrated to real firm data, while the parameters of the interest rate model are estimated by fitting the Euribor time series. To this aim, an ad hoc calibration procedure is developed which is based on the maximum likelihood principle and thus has the merit of being simple, fast and suitable for practical purposes. Our study reveals that the interest rate uncertainty reduces the valuation of investment projects. However, stochastic interest rates do not provide a substantial improvement with respect to constant interest rates, or at least the differences are not statistically significant.     

Robust games: theory and application to a Cournot duopoly model

In this paper, the robust game model proposed by Aghassi and Bertsimas (Math Program Ser B 107:231–273, 2006) for matrix games is extended to games with a broader class of payoff functions. This is a distribution-free model of incomplete information for finite games where players adopt a robust-optimization approach to contend with payoff uncertainty. They are called robust players and seek the maximum guaranteed payoff given the strategy of the others. Consistently with this decision criterion, a set of strategies is an equilibrium, robust-optimization equilibrium, if each player’s strategy is a best response to the other player’s strategies, under the worst-case scenarios. The aim of the paper is twofold. In the first part, we provide robust-optimization equilibrium’s existence result for a quite general class of games and we prove that it exists a suitable value \(\epsilon \) such that robust-optimization equilibria are a subset of \(\epsilon \)-Nash equilibria of the nominal version, i.e., without uncertainty, of the robust game. This provides a theoretical motivation for the robust approach, as it provides new insight and a rational agent motivation for \(\epsilon \)-Nash equilibrium. In the last part, we propose an application of the theory to a classical Cournot duopoly model which shows significant differences between the robust game and its nominal version.