Common Stochastic Factor Research Articles

The optimal strategy of the dynamic mean−variance problem for pairs trading with a common stochastic factor

The optimal strategy of the dynamic mean−variance problem for pairs trading with a common stochastic factor

ВПЛИВ СТОХАСТИЧНИХ ФАКТОРІВ НА ОПЕРАТИВНЕ УПРАВЛІННЯ ТРАНСПОРТНИМИ ПОТОКАМИ. ЧАСТИНА 2

The article describes the existing problems of uncertainty in the system of operational redistribution of traffic flows, considers stochastic factors that are different in nature and features of the effect on the transport system, which require consideration in the operational management of traffic flows, as well as the features of their influence on the short-term state of the transport system. A simplified classification of stochastic factors is given, algorithms for the connection of these factors with each other and with indicators that are already taken into account by the management system are given, the nature of the influence is indicated. Statistical data samples are analyzed and the basics of methods for working with them are indicated. For the most common stochastic factors, such as the number of traffic accidents on city road networks and weather and climatic features of the region, methods for generating graphic materials and mathematical approximations are proposed, and formulas for calculating some random variables are recommended, including using limits in the framework of the phase theory of traffic flows. Cartograms with the help of which it is possible to establish stochastic dependences of climatic changes and changes in the ecological state by the example of Mariupol are given. It is proposed for practical use a detailed block diagram of identifying stochastic factors, the formation of information arrays, their analysis and the supply of control signals to the operational management system. The diagram shows a clear differentiation of the primary and secondary stochastic data arrays, and their recommended links to the operational process control system of the transport process are indicated. Using the stated theoretical foundations, it becomes possible to increase the efficiency of the city’s transport system by optimizing the processes of the operational redistribution of traffic flows on the road network and making changes to short-term planning processes. Keywords: stochastic factors, road transport, traffic flow, transport system, transport planning, management, regulation.

On the memory of products of long range dependent time series

This paper derives the memory of the product series xtyt, where xt and yt are stationary long memory time series of orders dx and dy, respectively. Special attention is paid to the case of squared series and products of series driven by a common stochastic factor. It is found that the memory of products of series with non-zero means is determined by the maximal memory of the factor series, whereas the memory is reduced if the series are mean zero.

Pricing Recovery Risk via a Partial Information Transform

In his seminal paper, Wang ( S. S. Wang, A Universal Framework for Pricing Financial and Insurance Risks, ASTIN Bulletin, Volume 32, Issue 02 November 2002, pp 213-234) proposes a transform method to price both liabilities and contingent claims, whether traded or not. One application of the Wang Transform is in option pricing, which for example can be used in the structural modeling of defaultable bonds. The classical Merton model (R.C. Merton, On the pricing of corporate debt: The risk structure of interest rates, The Journal of Finance 29.2, 449-470, 1974.) assumes that default and post-default recoverable values are driven by a common stochastic factor, that of the firm's asset value. However, a single factor for pricing such bonds assumes that bond and equity returns are perfectly correlated, which need not be true. methods, (A. Cohen and N. Costanzino, Bond and CDS Pricing with Recovery Risk I and II, SSRN preprints) address the entanglement of recovery risk with default risk in the pricing of defaultable bonds. The authors show that this mixture can lead to errors in estimating the total risk that investors in these bonds have undertaken. The taken also considers related instruments such as CDS's and equity as well as solving the related boundary value problems for bond price. The time value of money is another important aspect of bond pricing, and in the same issue that Wang's paper appeared, Buhlmann (H. Buhlmann, New Math for Life Actuaries, ASTIN Bulletin, Volume 32, Issue 02 November 2002, pp 209-211.) proposed a paradigm shift in thinking about this technology. In his editorial, Buhlmann advocated switching to a based approach for teaching financial risk to actuaries. In our short note, we present a transform for a multifactor bond-pricing model that represents the partial information available to firm managers about recoverable value. In the spirit of Buhlmann's proposal, this is dependent on the choice of numeraire as well as the conditions for default. We will recover a version of the Wang Transform in the classical Merton model, and will calculate the transformed default probability in two other related structural models. The effect of this extra uncertainty about post-default recovery, we will see, can be observed through the distortion of the original default risk. Three examples are used to illuminate the approach, including a model that incorporates short-term credit spreads into asset and recovery value evolution.

Cointegration and Relative Value Arbitrage

This paper examines a new method of identifying close economic substitutes in the context of relative value arbitrage. We show that close economic substitutes correspond to a special case of cointegration whereby individual prices have approximately the same exposure to a common stochastic factor, or the cointegrating relation is approximately one-to-one. Empirical analysis of cointegration-based pairs trading shows that a metric of closeness constructed from the cointegrating relation strongly predicts the probability of convergence and profitability of pairs trades. Over period 1962-2013, a strategy that trades cointegrated pairs of near-parity generates average returns of 58 bps per month after trading costs, experiences 71% probability of convergence and outperform pairs that are selected using the conventional method of minimizing price distance. When extending to triplets trading, the predictability of the metric of closeness remains, however trading of cointegrated baskets of three stocks is less profitable due to smaller mispricings.

EFFICIENCY IN LARGE DYNAMIC PANEL MODELS WITH COMMON FACTORS

This paper deals with asymptotically efficient estimation in exchangeable nonlinear dynamic panel models with common unobservable factors. These models are relevant for applications to large portfolios of credits, corporate bonds, or life insurance contracts. For instance, the Asymptotic Risk Factor (ARF) model is recommended in the current regulation in Finance (Basel II and Basel III) and Insurance (Solvency II) for risk prediction and computation of the required capital. The specification accounts for both micro- and macrodynamics, induced by the lagged individual observations and the common stochastic factors, respectively. For large cross-sectional and time dimensionsnandT, we derive the efficiency bound and introduce computationally simple efficient estimators for both the micro- and macroparameters. The results are based on an asymptotic expansion of the log-likelihood function in powers of 1/n, and are linked to granularity theory. The results are illustrated with the stochastic migration model for credit risk analysis.

A flexible model of term-structure dynamics of commodity prices: a comparative analysis with a two-factor Gaussian model

This study compares two approaches to modeling a term structure of commodity prices. The first approach specifies the stochastic process of the underlying spot price and derives from the stipulated spot price dynamics valuation formulas of futures and other derivative contracts through no arbitrage. The second approach, as introduced by Smith [J. Appl. Econometr., 2005, 20, 405–422], is to model the dynamics of the entire futures curve directly by a set of common stochastic factors and to specify factor loadings by flexible functions of time-to-maturity and contract delivery month. Empirical applications of the models to four commodities (gold, crude oil, natural gas, and corn) reveal that the volatility of futures prices exhibits more complex dynamics than the pattern implied by the model stipulating a two-factor Gaussian process of the underlying spot price. Specifically, the flexible model of futures returns depicts the maturity effect and, particularly for the three consumption commodities, strong seasonal and cross-sectional variations in variance and covariance of concurrently traded contracts. Incorporating the depicted variance and covariance dynamics leads the flexible model of futures returns to suggest hedging strategies that are more effective than the strategies based on the conventional two-factor Gaussian model.

Why International Financial Markets are Not Cointegrated

Cointegration has frequently been used in the financial econometrics literature to assess the degree of interdependence of financial markets. We show that if individual stock prices are generated by random walks with possibly contemporaneously correlated innovations, the resulting indices cannot be cointegrated as they are a combination of n random walks which itself is non-stationary by construction. This result holds if (as in factor models) an additional common global or local random walk is allowed for. There will, however, never be less than n random walk components, as otherwise company specific characteristics would be ruled out to affect the stock price permanently. To substantiate the theoretical propositions we simulate stock prices (allowing for heteroscedasticity, correlated innovations and common factors), construct indices and test whether these indices are cointegrated. We show that while heteroscedasticity alone is able to mislead cointegration tests, it is not sufficient to explain at the same time the empirically found high correlation between stock market indices. A common stochastic factor as well as correlated price innovations are necessary to reproduce the empirical characteristic features. We conclude that cointegration is not a suitable method to analyze stock market interdependence.

Efficiency in Large Dynamic Panel Models with Common Factor

This paper deals with efficient estimation in exchangeable nonlinear dynamic panel models with common unobservable factor. The specification accounts for both micro- and macro-dynamics, induced by the lagged individual observation and the common stochastic factor, respectively. For large cross-sectional and time dimensions, and under a semiparametric identification condition, we derive the efficiency bound and introduce efficient estimators for both the micro- and macro-parameters. In particular, we show that the fixed effects estimator of the micro-parameter is not only consistent, but also asymptotically efficient. The results are illustrated with the stochastic migration model for credit risk analysis.

Quelle convergence financière pour les pecos ?

<titre>R&#233;sum&#233;</titre>&#192; travers la recherche d&#8217;une tendance stochastique commune dans l&#8217;&#233;volution des indices boursiers des pays en transition candidats en 2003 &#224; l&#8217;Union europ&#233;enne, cet article propose la recherche d&#8217;une forme de convergence entre les march&#233;s financiers de ces pays et entre ces march&#233;s et le march&#233; europ&#233;en. En prenant soin de neutraliser, gr&#226;ce &#224; l&#8217;expression des indices de march&#233;s dans une m&#234;me monnaie, les effets sp&#233;cifiques des perturbations mon&#233;taires locales, on met en &#233;vidence une tendance stochastique commune &#224; l&#8217;ensemble des march&#233;s des pecos, mais non pour l&#8217;ensemble &#233;largi incluant la zone euro. L&#8217;analyse de la tendance commune peut &#234;tre interpr&#233;t&#233;e en rapport avec l&#8217;avancement des r&#233;formes des march&#233;s financiers.

Stochastic Interest Rates and Price Discovery in Selected Commodity Markets

The temporal relationship between Chicago corn and soybean cash prices, nearby futures prices, and interest rates is examined using daily 1980-1989 data. Johansen cointegration tests suggest joint movement of the three series over the data period considered. In addition, analyses of individual crop years, which is consistent with previous work, shows co-movement between cash, futures, and interest rates in years when bivariate cointegration between cash and futures prices was not found. The results provide initial empirical evidence that a potential limitation of previous research in the study of cash- futures simple efficiency has been the exclusion of the interest rate as a common stochastic factor explaining equilibrium in models of cash and futures prices. (This abstract was borrowed from another version of this item.)