
on Computational Economics 
Issue of 2007‒01‒28
five papers chosen by 
By:  Algan, Yann; Allais, Olivier; Den Haan, Wouter 
Abstract:  A new algorithm is developed to solve models with heterogeneous agents and aggregate uncertainty that avoids some disadvantages of the prevailing algorithm that strongly relies on simulation techniques and is easier to implement than existing algorithms. A key aspect of the algorithm is a new procedure that parameterizes the crosssectional distribution, which makes it possible to avoid Monte Carlo integration. The paper also develops a new simulation procedure that not only avoids crosssectional sampling variation but is also more than ten times faster than the standard procedure of simulating an economy with a large but finite number of agents. This procedure can help to improve the efficiency of the most popular algorithm in which simulation procedures play a key role. 
Keywords:  incomplete markets; numerical solution; projection method; simulation 
JEL:  C63 D52 
Date:  2007–01 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:6062&r=cmp 
By:  Manfred Gilli (University of Geneva); Evis Këllezi (Mirabaud & cie); Hilda Hysi (University of Geneva  Department of Econometrics) 
Abstract:  In practical portfolio choice models risk is often defined as VaR, expected shortfall, maximum loss, Omega function, etc. and is computed from simulated future scenarios of the portfolio value. It is well known that the minimization of these functions can not, in general, be performed with standard methods. We present a multipurpose datadriven optimization heuristic capable to deal efficiently with a variety of risk functions and practical constraints on the positions in the portfolio. The efficiency and robustness of the heuristic is illustrated by solving a collection of real world portfolio optimization problems using different risk functions such as VaR, expected shortfall, maximum loss and Omega function with the same algorithm. 
Keywords:  Portfolio optimization, Heuristic optimization, Threshold accepting, Downside risk 
JEL:  C61 C63 G11 G32 
URL:  http://d.repec.org/n?u=RePEc:chf:rpseri:rp1&r=cmp 
By:  Arjan Lejour; Hugo RojasRomagosa 
Abstract:  Global applied general equilibrium (AGE) models focus on the interactions between regional product markets. Many of these models are developed to represent trade flows and evaluate trade policies. Foreign direct investment (FDI) and foreign commercial presence are ignored in most of them, although sales by foreign affiliates sometimes exceed the value of trade flows. This paper gives an overview of the scarce literature on modelling FDI in AGE models. Modelling options, data availability and simulation results are reviewed. Some conclusions are drawn for future work. 
Keywords:  CGE models; FDI; economic modelling 
JEL:  C68 F23 
Date:  2006–12 
URL:  http://d.repec.org/n?u=RePEc:cpb:memodm:169&r=cmp 
By:  Ulrich BrandtPollmann (Interdisciplinary Center for Scientific Computing, University of Heidelberg, Germany); Ralph Winkler (Center of Economic Research (CERETH) at ETH Zürich); Sebastian Sager (Interdisciplinary Center for Scientific Computing, University of Heidelberg, Germany); Ulf Moslener (Centre for European Economic Research (ZEW), Mannheim, Germany); Johannes P. Schlöder (Interdisciplinary Center for Scientific Computing, University of Heidelberg, Germany) 
Abstract:  We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateoftheart direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples. 
Keywords:  delayed differential equations, delayed optimal control, numerical optimization, timetobuild 
JEL:  C63 C61 
Date:  2006–10 
URL:  http://d.repec.org/n?u=RePEc:eth:wpswif:0659&r=cmp 
By:  FrancoisÉric Racicot (Département des sciences administratives, Université du Québec (Outaouais) et LRSP); Raymond Théoret (Département de stratégie des affaires, Université du Québec (Montréal)) 
Abstract:  Markets makers quote many option categories in terms of implicit volatility. In doing so, they can reactivate the Black and Scholes model which assumes that the volatility of an option underlying is constant while it is highly variable. First of all, this article, whose purpose is very empirical, presents a simulation of stochastic volatility programmed in Visual Basic (Excel) whose aim is to compute the price of an European option written on a zero coupon bond. We compare this computed price with this one resulting from Black analytical solution and we also show how to compute an interest rate forecast with the help of the simulation model. Then we write many Visual Basic and Matlab programs for the purpose of computing the implicit volatility surface, a threedimensional surface which can be plotted by using graphical capacities of Excel and Matlab. It remains that the concept of implicit volatility is very criticised because it is computed with the exercise price of an option and not with the price of the underlying, as it should be. Therefore, there are biases in the estimation of the «greeks» computed with implicit volatility. 
Keywords:  Financial engineering, Monte Carlo simulation, stochastic volatility, implicit volatility. 
JEL:  G12 G13 G33 
Date:  2007–01–01 
URL:  http://d.repec.org/n?u=RePEc:pqs:wpaper:012007&r=cmp 