The Vanishing Discount Factor Approach and Uniform Equilibrium in Absorbing Games

Employment creation in EU related to renewables expansion

Executive Stock Options Pricing with Free Wealth Weights and Continuous Partial Exercise: An Analytic Constrained Portfolio Optimization/Stochastic Discount Factor Approach

ABSTRACTIn the short run, there can be substantial differences in spot freight earnings between geographical regions of the global freight market for bulk carriers. Such differences can be consistent with an efficient market if they are temporary and if they cannot be exploited financially by pursuing chartering strategies that are based on publicly available information. In this paper, we apply a simple optimal switching model to evaluate whether such chartering strategies exist. We model the spot freight rate differential between the Atlantic and Pacific basins as a mean-reverting Ornstein–Uhlenbeck process and the entry–exit decision using the discount factor approach, which results in optimal trigger values for the entry/exit from each basin. Our empirical results suggest that the market is spatially efficient during normal freight market conditions when there is a surplus of vessels. The tight market conditions during the 2003–2008 freight market boom caused a persistent upward bias in Atlantic freight rates, but also here we find little added value from pursuing an active switching strategy.

Entry and exit decisions based on a discount factor approach

In this paper, we study the properties of portfolios and discount factor bounds in the presence of conditioning information. The main contribution of this paper is to provide a detailed comparison between various stochastic discount factor bounds with conditioning information. We do this by exploiting the explicit link between the stochastic discount factor approach and portfolio efficiency in the presence of conditioning information. For common choices of base assets and conditioning instruments, we find that the unconditionally efficient bounds of Ferson and Siegel (2002) are statistically indistinguishable from the (theoretically) optimal bounds of Gallant, Hansen, and Tauchen (1990), while having smaller sampling variability. We demonstrate that the difference in sampling variability of the UE and GHT bounds is due to the different behavior of the portfolio weights underlying their construction. Our work is closely related to and extends Ferson and Siegel (2001), Ferson and Siegel (2002) and Bekaert and Liu (2001).

We propose a multivariate test based on no-arbitrage conditions under the stochastic discount factor approach, which compares cross-sectional variation in equity returns to the cross-sectional variation in their conditional covariance with the discount factors. Using the multivariate generalized heteroskedasticity in mean model to estimate the 25 portfolios formed on size and book-to-market ratio, together each with its own arbitrage condition, we find that the no-arbitrage test rejects the consumption-based capital asset pricing model (C-CAPM). Although the conditional covariances of returns with consumption exhibit negative variation across size, they do not vary across the book-to-market ratio. Thus, the C-CAPM can capture size effect, but not value effect. Allowing the coefficients on the consumption covariances to be different largely improves the fit of the C-CAPM, however. The value effect appears to be associated with book-to-market ratio as well as size. Book-to-market ratio separately does not generate information about average returns that cannot be explained by the C-CAPM. One possible explanation for this extra dimension of risk is the investment growth prospect of firms. Low book-to-market ratio firms may be expected to have higher rates of growth while small firms may also be expected to behave similarly.

Nominal exchange rates in low-inflation advanced countries are nearly random walks. Engel and West (2003a) offer an explanation for this in the context of models in which the exchange rate is determined as the discounted sum of current and expected future fundamentals. Engel and West show that if the fundamentals are I(1), then as the discount factor approaches one, the exchange rate becomes indistinguishable from a random walk. An alternative explanation for the random-walk behavior of exchange rates is that there are some unobserved variables that drive exchange rates that follow near random walks. This paper takes the approach that both explanations are possible. We are able to measure how much of exchange-rate variation could be accounted for by the Engel-West explanation, despite the fact that we do not observe the information set of financial markets. We find that the observable fundamentals (money, income, prices, interest rates) may account for about 40 percent of the variance of changes in exchange rates under the assumption of discount factors near unity.

Multi-regional clinical trial (MRCT) has become an increasing trend for its supporting simultaneous global drug development. After MRCT, consistency assessment needs to be conducted to evaluate regional efficacy. The weighted Z-test approach is a common consistency assessment approach in which the weighting parameter W does not have a good practical significance; the discounting factor approach improved from the weighted Z-test approach by converting the estimation of W in original weighted Z-test approach to the estimation of discounting factor D. However, the discounting factor approach is an approach of frequency statistics, in which D was fixed as a certain value; the variation of D was not considered, which may lead to un-reasonable results. In this paper, we proposed a Bayesian approach based on D to evaluate the treatment effect for the target region in MRCT, in which the variation of D was considered. Specifically, we first took D random instead of fixed as a certain value and specified a beta distribution for it. According to the results of simulation, we further adjusted the Bayesian approach. The application of the proposed approach was illustrated by Markov Chain Monte Carlo simulation.

This paper develops asymptotic econometric theory to help understand data generated by a present value model with a discount factor near one. A leading application is to exchange rate models. A key assumption of the asymptotic theory is that the discount factor approaches 1 as the sample size grows. The finite sample approximation implied by the asymptotic theory is quantitatively congruent with modest departures from random walk behavior with imprecise estimation of a well-studied regression relating spot and forward exchange rates.

We analyze hedge fund performance using the stochastic discount factor (SDF) approach and imposing the arbitrage-free requirement to correctly value the derivatives and dynamic trading strategies used by hedge funds. Using SDFs of many asset-pricing models, we evaluate hedge fund portfolios based on style and characteristics. Without the arbitrage-free requirement, pricing errors are relatively small and a few models can explain hedge fund returns. With this requirement, pricing errors are much bigger, and all models fail to price style and volatility portfolios. Fund manager characteristics like age, experience, and education explain some of the mispricing of our best risk model.

Each of $n$ arms generates an infinite sequence of Bernoulli random variables. The parameters of the sequences are themselves random variables, and are independent with a common distribution satisfying a mild regularity condition. At each stage we must choose an arm to observe (or pull) based on past observations, and our aim is to maximize the expected discounted sum of the observations. In this paper it is shown that as the discount factor approaches one the optimal policy tends to the rule of least failures, defined as follows: pull the arm which has incurred the least number of failures, or if this does not define an arm uniquely select from amongst the set of arms which have incurred the least number of failures an arm with the largest number of successes.

In this paper, a recursive training procedure with forgetting factor is proposed for on-line calibration of temporal neural networks. The forgetting factor discounts old measurements through an on-line model calibration. The forgetting factor approach enables the recursive algorithm to reduce the effect of the older error data by multiplying the error data by a discounting factor. The proposed procedure is used to calibrate a temporal neural network for reservoir inflow modeling. The mean monthly inflow of the Karoon-III reservoir dam in the south-western part of Iran is used to test the performance of the proposed approach. An autoregressive moving average (ARMA) model is also applied to the same data. The temporal neural network, which is trained with the proposed approach, has shown a significant improvement in the forecast accuracy in comparison with the network trained by the conventional method. It is also demonstrated that the neural network trained with forgetting factor results in better forecasts compared to the statistical ARMA model, which has been calibrated through this approach.

In the perfect and unrealistic Black and Scholes (J Polit Econ 81:637–659, 1973) world, the dynamics \((S_{t})_{t\in [0,T]}\) of the risky asset, under the historical probability \(\mathbb{P}\), is given by the following stochastic differential equation: $$\displaystyle{ dS_{t} =\mu S_{t}dt +\sigma S_{t}dW_{t} }$$ where \((W_{t})_{t\in [0,T]}\) is a standard Brownian motion under \(\mathbb{P}\). In this case, there is no ambiguity in the definition the arbitrage-free price of any European contingent claim with maturity T. In fact, in this complete market which is set in continuous time, this value is none other than the value of any replicating portfolio. Moreover, prices may be expressed in terms of conditional expectations under a unique equivalent martingale measure Q whose density with respect to the historical probability is given by the Girsanov theorem $$\displaystyle{ \frac{dQ} {d\mathbb{P}} = e^{-\frac{\mu -r} {\sigma } W_{T}-\left (\frac{\mu -r} {\sigma } \right )^{2} \frac{T} {2} } }$$ where r is the constant and continuously compound risk-free rate. Unfortunately, as we have seen in Sect. 2.1, the restrictive underlying hypotheses (constant volatility, independent increments, Gaussian log-returns, etc…) are questioned by many empirical studies and GARCH models appear as excellent alternative solutions to potentially overcome some well-documented systematic biases associated with the Black and Scholes model.

An Empirical Study on the Stock Price Reaction to Earnings Announcements using the Stochastic Discount Factor Approach

This study focuses on the diversification benefits of the most developed equity markets of Central and Eastern Europe (CEE). To evaluate these benefits of diversification we use so-called spanning tests based on a stochastic discount factor approach and estimated by General Methods of Moments (GMM). Spanning tests investigate whether the returns of test assets (in our case the returns of CEE equity markets) can be mimicked by the returns of some benchmark assets. If this is possible adding the test assets to the set of the benchmark assets does not improve the mean-variance efficient frontier. In recent studies as for example DeSantis (1994), Harvey (1995) or Bekaert/Urias (1996) spanning tests have been successfully applied to emerging equity markets but these studies do not cover the emerging equity markets of Central and Eastern Europe. In addition our study addresses the diversification benefits not only for U.S. investors, as is the usual case in these empirical studies, but extends the analysis on British and German investors, too. A third feature that distinguishes our investigation from most other studies on this topic is the analysis of the effects of currency hedging on diversification benefits. At a quick glance the CEE equity markets seem to offer significant and high diversification benefits. But this picture becomes cloudy after a thorough analysis. Only the equity markets of the Czech Republic, Slovakia and Slovenia contribute significantly to the diversification benefits. But a realisation of these benefits would imply to have not only long but also short positions in CEE equities. Taken into account transaction costs and limited access to futures and options markets it seems to be very doubtful that the theoretical diversification benefits can actually be realised. This result is in correspondence with recent studies on other emerging markets such as DeRoon/Nijman/Werker (2000). The results of the study also show that the home currency of the investor is of some importance for the results of the spanning tests. The outcomes for British, German and U.S. investors are similar but not identical. Therefore it seems to be useful to analyse benefits of diversification not only from the point of view of U.S. investors but to take explicitly into account the currency of the investor. Another interesting result is that currency hedging clearly improves the possible performance of an investment in CEE equity markets. What is now the consequence for investors that consider an investment in CEE equity markets? Our study comes to the result that a buy-and-hold investor could hardly benefit from such an investment. Only investors that have superior timing capabilities could profit from the remarkably strong swings in the levels of CEE equity indices in the past.