Is There a Curse of Dimensionality for Contraction Fixed Points in the Worst Case?

This paper analyzes the complexity of the contraction fixed point problem: compute an ɛ-approximation to the fixed point V*Γ(V*) of a contraction mapping Γ that maps a Banach space Bd of continuous functions of d variables into itself. We focus on quasi linear contractions where Γ is a nonlinear functional of a finite number of conditional expectation operators. This class includes contractive Fredholm integral equations that arise in asset pricing applications and the contractive Bellman equation from dynamic programming. In the absence of further restrictions on the domain of Γ, the quasi linear fixed point problem is subject to the curse of dimensionality, i.e., in the worst case the minimal number of function evaluations and arithmetic operations required to compute an ε-approximation to a fixed point V*∈Bd increases exponentially in d. We show that the curse of dimensionality disappears if the domain of Γ has additional special structure. We identify a particular type of special structure for which the problem is strongly tractable even in the worst case, i.e., the number of function evaluations and arithmetic operations needed to compute an ɛ-approximation of V* is bounded by Cɛ−p where C and p are constants independent of d. We present examples of economic problems that have this type of special structure including a class of rational expectations asset pricing problems for which the optimal exponent p1 is nearly achieved

Economic and accounting rates of return

The rate of return on invested capital is a central concept in financial analysis. The purpose of calculating the rate of return on investment in general is to measure the financial performance, to assess the desirability of a project and to make decisions on the valuation of firms. Financial statement users make regular use of the accounting rate of return (ARR) rather than the economic rate of return (IRR) to assess the performance of corporations and public-sector enterprises, to evaluate capital investment projects, and to price financial claims such as shares. Since ARR measures are based on published accounting statements, there has been a long and sometimes heated debate as to whether such measures have any economic significance. This paper aims to provide a summary of the economic and accounting rates of return discussions in the literature. We analyze the concepts of ARR and IRR and explore possible relationships between them. We extend the previous studies in this line to provide more specific relations of IRR and ARR.

A Stochastic discount factor approach to asset pricing using panel data asymptotics

Using the Pricing Equation in a panel-data framework, we construct a novelconsistent estimator of the stochastic discount factor (SDF) which relies on thefact that its logarithm is the "common feature" in every asset return of theeconomy. Our estimator is a simple function of asset returns and does notdepend on any parametric function representing preferences.The techniques discussed in this paper were applied to two relevant issues inmacroeconomics and finance: the first asks what type of parametric preference-representation could be validated by asset-return data, and the second askswhether or not our SDF estimator can price returns in an out-of-sample forecasting exercise.In formal testing, we cannot reject standard preference specifications used inthe macro/finance literature. Estimates of the relative risk-aversion coefficientare between 1 and 2, and statistically equal to unity.We also show that our SDF proxy can price reasonably well the returns ofstocks with a higher capitalization level, whereas it shows some difficulty inpricing stocks with a lower level of capitalization.

Multilevel Monte Carlo methods for applications in finance

Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the key features in achieving a high rate of multilevel variance convergence, and suggests directions for future research.Comment: arXiv admin note: text overlap with arXiv:1202.6283; and with arXiv:1106.4730 by other author

Using CAViaR models with implied volatility for value-at-risk estimation

This paper proposes VaR estimation methods that are a synthesis of conditional autoregressive value at risk (CAViaR) time series models and implied volatility. The appeal of this proposal is that it merges information from the historical time series and the different information supplied by the market’s expectation of risk. Forecast combining methods, with weights estimated using quantile regression, are considered. We also investigate plugging implied volatility into the CAViaR models, a procedure that has not been considered in the VaR area so far. Results for daily index returns indicate that the newly proposed methods are comparable or superior to individual methods, such as the standard CAViaR models and quantiles constructed from implied volatility and the empirical distribution of standardised residual. We find that the implied volatility has more explanatory power as the focus moves further out into the left tail of the conditional distribution of S&P500 daily returns

Measuring systemic risk

We present a simple model of systemic risk and show how each financial institution’s contribution to systemic risk can be measured and priced. An institution’s contribution, denoted systemic expected shortfall (SES), is its propensity to be undercapitalized when the system as a whole is undercapitalized, which increases in its leverage, volatility, correlation, and tail-dependence. Institutions internalize their externality if they are “taxed” based on their SES. Through several examples, we demonstrate empirically the ability of components of SES to predict emerging systemic risk during the nancial crisis of 2007-2009.Systemic risk ; Risk

Revealing the arcane: an introduction to the art of stochastic volatility models

This essay is aimed to provide a straightforward and sufficiently accessible demonstration of some known procedures for stochastic volatility model. It reviews the important related concepts, gives informal derivations of the methods and can be useful as a cookbook for a novice. The exposition is confined to classical (non-Bayesian) framework and discrete-time formulations.stochastic volatility

Managing Exchange Rate Volatility: A Comparative Counterfactual Analysis of Singapore 1994 to 2003

The objective of this paper is see how well Singapore’s exchange rate regime has coped with exchange rate volatility before and after the Asian financial crisis by comparing the performance of Singapore’s actual regime in minimising the volatility of the nominal effective exchange rate (NEER) and the bilateral rate against the US$ against some counterfactual regimes and the corresponding performance of eight other East Asian countries. In contrast to previous counterfactual exercises, such as Williamson (1998a) and Ohno (1999) which compute the weights for effective exchange rates on the basis of simple bloc aggregates, we apply a more disaggregated methodology using a larger number of trade partners. We also utilize ARCH/GARCH techniques to obtain estimates of heteroskedastic variances to better capture the time-varying characteristics of volatility for the actual and simulated exchange rate regimes. Our findings confirm that Singapore’s managed floating exchange rate system has delivered relatively low currency volatility. Although there are gains in volatility reduction for all countries in the sample from the adoption of either a unilateral or common basket peg, particularly post-crisis, these gains are relatively low for Singapore, largely because low actual volatility. Finally, there are additional gains for nondollar peggers from stabilizing intra-EA exchange rates against the dollar if they were to adopt a basket peg, especially post-crisis, but the gains for Singapore are again relatively modest.East Asia, exchange rates, counterfactuals.