The thesis consists of four chapters. The introductory chapter clarifies different notions of rationality used by economists and gives a summary of the remainder of the thesis. Chapter 2 proposes an explanation for the common empirical observation of the coexistence of infrequently-changing regular price ceilings and promotion-like price patterns. The results derive from enriching an otherwise standard, albeit stylized, general equilibrium model with two elements. First, the consumer-producer interaction is modeled in the spirit of the price dispersion literature, by introducing oligopolistic markets, consumer search costs and heterogeneity. Second, consumers are assumed to be boundedly-rational: In order to incorporate new information about the general price level, they have to incur a small cognitive cost. The decision whether to re-optimize or act according to the obsolete knowledge about prices is itself a result of optimization. It is shown that in this economy, individual retail prices are capped below the monopoly price, but are otherwise flexible. Moreover, they have the following three properties: 1) An individual price has a positive probability of being equal to the ceiling. 2) Prices have a tendency to fall below the ceiling and then be reset back to the cap value. 3) The ceiling remains constant for extended time intervals even when the mean rate of inflation is positive. Properties 1) and 2) can be associated with promotions and properties 1) and 3) imply the emergence of nominal price rigidity. The results do not rely on any type of direct costs of price adjustment. Instead, price stickiness derives from frictions on the consumers’ side of the market, in line with the results of several managerial surveys. It is shown that the developed theory, compared to the classic menu costs-based approach, does better in matching the stylized facts about the reaction of individual prices to inflation. In terms of quantitative assessment, the model, when calibrated to realistic parameter values, produces median price ceiling durations that match values reported in empirical studies.<p><p>The starting point of the essay in Chapter 3 is the observation that the baseline New-Keynesian model, which relies solely on the notion of infrequent price adjustment, cannot account for the observed degree of inflation sluggishness. Therefore, it is a common practice among macro- modelers to introduce an ad hoc additional source of persistence to their models, by assuming that price setters, when adjusting a price of their product, do not set it equal to its unobserved individual optimal level, but instead catch up with the optimal price only gradually. In the paper, a model of incomplete adjustment is built which allows for explicitly testing whether price-setters adjust to the shocks to the unobserved optimal price only gradually and, if so, measure the speed of the catching up process. According to the author, a similar test has not been performed before. It is found that new prices do not generally match their estimated optimal level. However, only in some sectors, e.g. for some industrial goods and services, prices adjust to this level gradually, which should add to the aggregate inflation sluggishness. In other sectors, particularly food, price-setters seem to overreact to shocks, with new prices overshooting the optimal level. These sectors are likely to contribute to decreasing the aggregate inflation sluggishness. Overall, these findings are consistent with the view that price-setters are boundedly-rational. However, they do not provide clear-cut support for the existence of an additional source of inflation persistence due to gradual individual price adjustment. Instead, they suggest that general equilibrium macroeconomic models may need to include at least two types of production sectors, characterized by a contrasting behavior of price-setters. An additional finding stemming from this work is that the idiosyncratic component of the optimal individual price is well approximated by a random walk. This is in line with the assumptions maintained in most of the theoretical literature. <p><p>Chapter 4 of the thesis has been co-authored by Julia Lendvai. In this paper a full-fledged production economy model with Kahneman and Tversky’s Prospect Theory features is constructed. The agents’ objective function is assumed to be a weighted sum of the usual utility over consumption and leisure and the utility over relative changes of agents’ wealth. It is also assumed that agents are loss-averse: They are more sensitive to wealth losses than to gains. Apart from the changes in the utility, the model is set-up in a standard Real Business Cycle framework. The authors study prices of stocks and risk-free bonds in this economy. Their work shows that under plausible parameterizations of the objective function, the model is able to explain a wide set of unconditional asset return moments, including the mean return on risk-free bonds, equity premium and the Sharpe Ratio. When the degree of loss aversion in the model is additionally assumed to be state-dependent, the model also produces countercyclical risk premia. This helps it match an array of conditional moments and in particular the predictability pattern of stock returns. / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

This thesis presents the main results of my research in the field of computational finance and portfolios optimization. We focus on pricing Asian basket options and portfolio problems in the presence of inflation with stochastic interest rates.<p><p>In Chapter 2, we concentrate upon the derivation of bounds for European-style discrete arithmetic Asian basket options in a Black and Scholes framework.We start from methods used for basket options and Asian options. First, we use the general approach for deriving upper and lower bounds for stop-loss premia of sums of non-independent random variables as in Kaas et al. [Upper and lower bounds for sums of random variables, Insurance Math. Econom. 27 (2000) 151–168] or Dhaene et al. [The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom. 31(1) (2002) 3–33]. We generalize the methods in Deelstra et al. [Pricing of arithmetic basket options by conditioning, Insurance Math. Econom. 34 (2004) 55–57] and Vanmaele et al. [Bounds for the price of discrete sampled arithmetic Asian options, J. Comput. Appl. Math. 185(1) (2006) 51–90]. Afterwards we show how to derive an analytical closed-form expression for a lower bound in the non-comonotonic case. Finally, we derive upper bounds for Asian basket options by applying techniques as in Thompson [Fast narrow bounds on the value of Asian options, Working Paper, University of Cambridge, 1999] and Lord [Partially exact and bounded approximations for arithmetic Asian options, J. Comput. Finance 10 (2) (2006) 1–52]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity<p><p>In Chapter 3, we propose some moment matching pricing methods for European-style discrete arithmetic Asian basket options in a Black & Scholes framework. We generalize the approach of Curran M. (1994) [Valuing Asian and portfolio by conditioning on the geometric mean price”, Management science, 40, 1705-1711] and of Deelstra G. Liinev J. and Vanmaele M. (2004) [Pricing of arithmetic basket options by conditioning”, Insurance: Mathematics & Economics] in several ways. We create a framework that allows for a whole class of conditioning random variables which are normally distributed. We moment match not only with a lognormal random variable but also with a log-extended-skew-normal random variable. We also improve the bounds of Deelstra G. Diallo I. and Vanmaele M. (2008). [Bounds for Asian basket options”, Journal of Computational and Applied Mathematics, 218, 215-228]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and<p>time-to-maturity.<p><p>In Chapter 4, we use the stochastic dynamic programming approach in order to extend<p>Brennan and Xia’s unconstrained optimal portfolio strategies by investigating the case in which interest rates and inflation rates follow affine dynamics which combine the model of Cox et al. (1985) [A Theory of the Term Structure of Interest Rates, Econometrica, 53(2), 385-408] and the model of Vasicek (1977) [An equilibrium characterization of the term structure, Journal of Financial Economics, 5, 177-188]. We first derive the nominal price of a zero coupon bond by using the evolution PDE which can be solved by reducing the problem to the solution of three ordinary differential equations (ODE). To solve the corresponding control problems we apply a verification theorem without the usual Lipschitz assumption given in Korn R. and Kraft H.(2001)[A Stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40(4), 1250-1269] or Kraft(2004)[Optimal Portfolio with Stochastic Interest Rates and Defaultable Assets, Springer, Berlin].<p><p><p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished