Asymptotic asset pricing and bubbles

We define the concept of asymptotic superreplication, and prove a duality principle of asset pricing for sequences of financial markets (e.g., weakly converging financial markets and large financial markets) based on contiguous sequences of equivalent local martingale measures. This provides a pricing mechanism to calculate the fundamental value of a financial asset in the asymptotic market. We introduce the notion of asymptotic bubbles by showing that this fundamental value can be strictly lower than the current price of the asset. In the case of weakly converging markets, we show that this fundamental value is equal to an expectation of the terminal value of the asset in the weak-limit market. From a practical perspective, we relate the asymptotic superreplication price to a limit of quantile-hedging prices. This shows that even when a price process is a true martingale, it can have properties similar to a bubble, up to a set of small probability. For practical applications, we give examples of weakly converging discrete-time models (e.g. some GARCH models) and large financial models that present bubbles.     

A model of speculative behaviour with a strange attractor

An asset pricing model for a speculative financial market with fundamentalists and chartists is analysed. The model explains bursts of volatility in financial markets, which are not well explained by the traditional finance paradigms. Speculative bubbles arise as a complex non-linear dynamic phenomenon brought about naturally by the dynamic interaction of heterogeneous market participants. Depending on the time lag in the formation of chartists' expectations, the system evolves through several dynamic regimes, finishing in a strange attractor. Chaos provides a self-sustained motion around the rationally expected equilibrium that corresponds to a speculative bubble. In order to explain the role of Chartism, chaotic motion is a very interesting theoretical feature for a speculative financial market model. It provides a complex non-linear dynamic behaviour around the Walrasian equilibrium price produced by deterministic interactions between fundamentalists and chartists. This model could be a link between two opposite views over the behaviour of financial markets: the theorist's literature view that claims the random motion of asset prices, and the chartist's position extensively adopted by market professionals.     

The Dynamic Interaction of Speculation and Diversification

A discrete time model of a financial market is developed, in which heterogeneous interacting groups of agents allocate their wealth between two risky assets and a riskless asset. In each period each group formulates its demand for the risky assets and the risk‐free asset according to myopic mean‐variance maximizazion. The market consists of two types of agents: fundamentalists, who hold an estimate of the fundamental values of the risky assets and whose demand for each asset is a function of the deviation of the current price from the fundamental, and chartists, a group basing their trading decisions on an analysis of past returns. The time evolution of the prices is modelled by assuming the existence of a market maker, who sets excess demand of each asset to zero at the end of each trading period by taking an offsetting long or short position, and who announces the next period prices as functions of the excess demand for each asset and with a view to long‐run market stability. The model is reduced to a seven‐dimensional nonlinear discrete‐time dynamical system, that describes the time evolution of prices and agents' beliefs about expected returns, variances and correlation. The unique steady state of the model is determined and the local asymptotic stability of the equilibrium is analysed, as a function of the key parameters that characterize agents' behaviour. In particular it is shown that when chartists update their expectations sufficiently fast, then the stability of the equilibrium is lost through a supercritical Neimark–Hopf bifurcation, and self‐sustained price fluctuations along an attracting limit cycle appear in one or both markets. Global analysis is also performed, by using numerical techniques, in order to understand the role played by the chartists' behaviour in the transition to a regime characterized by irregular oscillatory motion and coexistence of attractors. It is also shown how changes occurring in one market may affect the price dynamics of the alternative risky asset, as a consequence of the dynamic updating of agents' portfolios.     

On the role of heterogeneous and imperfect information in a laboratory financial market

In this paper, we analyze the behavior of a group of heterogeneously informed investors in an laboratory asset market. Our experimental setting is inspired by Huber et al. (On the benefit of information in markets with heterogeneously informed traders: an experimental study, 2004). However, instead of their system of cumulative and exogenously given information structure, we introduce an information market where the traders can buy an imperfect prediction of the future value of the dividend with a maximum anticipation of four periods. The accuracy of the prediction decreases with the chosen time horizon, whereas its price remains constant. Our results confirm a non-strictly monotonic increasing value of the information.     

Expectation formation in an experimental foreign exchange market

Participants of an experimental foreign exchange market forecast an exchange rate with an unknown price reaction function. Aggregate demand is derived from their own forecasts and random shocks. Our experimental results indicate that the expectations of the subjects tend to be coordinated on a common prediction strategy. This strategy is best described as a trend-extrapolative, destabilizing expectation formation scheme. Deviations from common expectations are mainly caused by random shocks, which can be ascribed to the similarity of the subjects’ behavior within and between the different markets. The findings can be explained using insights of behavioral economics.     

基于异质交易者定价模型的资产价格泡沫内生机理研究

资产价格泡沫等市场异常现象使得有效市场假说理论受到质疑,研究者们更多的是从行为金融学的角度对这些现象进行解释,认为是由市场投资者的非理性因素所造成的。本文考虑了市场中投资者决策的异质性,构建了含有长期基础投资者和短期技术投资者的异质交易模型,以说明在投资者均具有理性预期的条件下,有效市场假说理论同样可以解释泡沫的产生。具体而言,技术投资者的交易行为使价格产生波动,基础投资者的存在则对波动起到放大作用,并会进一步导致泡沫的出现,随着基础投资者所占的比例增大,泡沫膨胀的速度加快,由此导致市场的波动越剧烈。研究结果为市场监管者提供了有益的启示:与其设置壁垒限制技术投资者的加入及交易活动,不如让越来越多的技术投资者加入到市场中来,这样更有益于市场的稳定。     

Time Charters with Purchase Options in Shipping: Valuation and Risk Management

Abstract

The article studies the valuation and optimal management of Time Charters with Purchase Options (T/C–POPs), which is a specific type of asset lease with embedded options that is common in shipping markets. T/C–POPs are economically significant and sometimes account for more than half of the stock market value of listed shipping companies.

The main source of risk in markets for maritime transportation is the freight rate, and we therefore specify a single-factor continuous time model for the dynamic evolution of freight rates that allows us to price a wide variety of freight rate-related derivatives including various forms of T/C–POPs using contingent claims valuation techniques. Our model allows for the derivation of closed valuation formulas for some simple freight rate derivatives, whereas the more complex ones are analysed using numerical (finite difference) procedures. We accompany our theoretical results with illustrative numerical examples as we proceed.     

An investigation of stock price dynamics in emerging markets

The emergence of stock markets in former centrally planned economies poses a significant problem to financial economists and policy makers in that price movements in these markets are not well explained by conventional capital theory. The opening of stock markets brings about a new equilibrium value P̂ for the firm. Shares are floated on an estimate of P̂, and buyers of these shares and individuals trading in the secondary market are also obliged to do so on the basis of their estimates of this magnitude. At any time, the market price of the firm's shares then reflects the market's best guess of what its value would be in the new equilibrium, and information on which to calculate estimates become more readily available as the stock market matures. This paper presents a stochastic price model which takes all of these factors into consideration. The model also provides a theoretical foundation underlying the pronounced trends of prices in emerging stock markets, and explains why they appear to be so volatile. © 1998 John Wiley & Sons, Ltd.     

Mean–Variance Optimal Adaptive Execution

Abstract

Electronic trading of equities and other securities makes heavy use of ‘arrival price’ algorithms that balance the market impact cost of rapid execution against the volatility risk of slow execution. In the standard formulation, mean–variance optimal trading strategies are static: they do not modify the execution speed in response to price motions observed during trading. We show that substantial improvement is possible by using dynamic trading strategies and that the improvement is larger for large initial positions.

We develop a technique for computing optimal dynamic strategies to any desired degree of precision. The asset price process is observed on a discrete tree with an arbitrary number of levels. We introduce a novel dynamic programming technique in which the control variables are not only the shares traded at each time step but also the maximum expected cost for the remainder of the program; the value function is the variance of the remaining program. The resulting adaptive strategies are ‘aggressive-in-the-money’: they accelerate the execution when the price moves in the trader's favor, spending parts of the trading gains to reduce risk.     

Determination of the Probability Distribution Measures from Market Option Prices Using the Method of Maximum Entropy in the Mean

Abstract

We consider the problem of recovering the risk-neutral probability distribution of the price of an asset, when the information available consists of the market price of derivatives of European type having the asset as underlying. The information available may or may not include the spot value of the asset as data. When we only know the true empirical law of the underlying, our method will provide a measure that is absolutely continuous with respect to the empirical law, thus making our procedure model independent. If we assume that the prices of the derivatives include risk premia and/or transaction prices, using this method it is possible to estimate those values, as well as the no-arbitrage prices. This is of interest not only when the market is not complete, but also if for some reason we do not have information about the model for the price of the underlying.     

Nonmyopic optimal portfolios in viable markets

We provide a representation for the nonmyopic optimal portfolio of an agent consuming only at the terminal horizon when the single state variable follows a general diffusion process and the market consists of one risky asset and a risk-free asset. The key term of our representation is a new object that we call the “rate of macroeconomic fluctuation” whose properties are fundamental for the portfolio dynamics. We show that, under natural cyclicality conditions, (i) the agent’s hedging demand is positive (negative) when the product of his prudence and risk tolerance is below (above) two and (ii) the portfolio weights decrease in risk aversion. We apply our results to study a general continuous-time capital asset pricing model and show that under the same cyclicality conditions, the market price of risk is countercyclical and the price of the risky asset exhibits excess volatility.     

A note on arbitrage,approximate arbitrage and the fundamental theorem of asset pricing

We provide a critical analysis of the proof of the fundamental theorem of asset pricing given in the paper Arbitrage and approximate arbitrage: the fundamental theorem of asset pricing by B. Wong and C.C. Heyde [Stochastics 82 (2010), pp. 189–200] in the context of incomplete Itô-process models. We show that their approach can only work in the known case of a complete financial market model and give an explicit counter example.     

An evolutionary alternative to rational expectations models of stock markets

Recent time series analyses of stock returns suggest that they contain persistent, mean-reverting stochastic trends, a results that is difficult to explain with traditional rational expectations models of stock markets. A simple model of asset pricing, which uses results on the dynamics of evolutionary games, provides a possible micro-economic foundation for this result.     

A cellation of the Grassmann manifold

Motivated by the computation of equilibria in economic models with incomplete asset markets, a cellation of the Grassmann manifold is constructed by restricting a common atlas. The Grassmann manifold ofm-planes inn-dimensional space is shown to be a union ofn choosem congruentm(n−m)-dimensional topological disks whose interiors are disjoint.     

Chaotic dynamics in agricultural markets

In a recent article, Chiarella [7] used a nonlinear supply curve with exactly one inflection point in the context of a cobweb model in order to make plausible that chaotic behaviour may result in such a model. There is, however, no exact proof under what conditions chaos can actually show up since Chiarella confines the analysis to a second order approximation to his difference equation. In a somewhat different model (a linear supply and a nonlinear demand curve which can be given a microeconomic foundation) we show that, under the formation of adaptive price expectations, the resulting adjustment mechanism can generate a wide range of dynamic behaviour (depending on the prevailing parameter constellations) such as stability, bifurcations with stable cycles of period 2, 4, 8, ... and, finally, aperiodic time paths, (i.e. we can show that period-3 cycles exist). In a second step, long historical time series of weekly price observations in German agricultural markets are scrutinized with regard to the hypothesis of nonlinearities. We study their correlation dimensions only recently employed by economists as a characteristic measure which allows, under certain conditions, to distinguish between deterministic chaos and random noise. Our results do not provide evidence to reject the hypothesis, although noise infection of the series cannot be ruled out.     

Integrated simulation and optimization models for tracking international fixed income indices

Portfolio managers in the international fixed income markets must address jointly the interest rate risk in each market and the exchange rate volatility across markets. This paper develops integrated simulation and optimization models that address these issues in a common framework. Monte Carlo simulation procedures generate jointly scenarios of interest and exchange rates and, thereby, scenarios of holding period returns of the available securities. The portfolio manager’s risk tolerance is incorporated either through a utility function or a (modified) mean absolute deviation function. The optimization models prescribe asset allocation weights among the different markets and also resolve bond-picking decisions. Therefore several interrelated decisions are cast in a common framework. Two models – an expected utility maximization and a mean absolute deviation minimization – are implemented and tested empirically in tracking a composite index of the international bond markets. Backtesting over the period January 1997 to July 1998 illustrate the efficacy of the optimization models in dealing with uncertainty and tracking effectively the volatile index. Of particular interest is the empirical demostration that the integrative models generate portfolios that dominate the portfolios obtained using classical disintegrated approaches. Received: November 24, 1998 / Accepted: October 1, 2000?Published online December 15, 2000     

Optimal procurement strategies for online spot markets

Spot markets have emerged for a broad range of commodities, and companies have started to use them in addition to their traditional, long-term procurement contracts (forward contracts). In comparison to forward contracts, spot markets offer products at essentially negligible lead time, but typically command a higher expected price for this added flexibility while also exhibiting substantial price uncertainty. In our research, we analyze the resulting procurement challenge and quantify the benefits of using spot markets from a supply chain perspective. We develop and solve mathematical models that determine the optimal order quantity to purchase via forward contracts and the optimal quantity to purchase via spot markets. We analyze the most general situation where commodities can be both bought and sold via a spot market and derive closed-form results for this case. We compare the obtained results to the reference scenario of pure contract sourcing and we include results for situations where the use of spot markets is restricted to either buying or selling only. Our approaches can be used by decision makers to determine optimal procurement strategies based on key parameters such as, demand and spot price volatilities, correlation between demand and spot prices, and risk aversion. The results of our analysis demonstrate that significant profit improvements can be achieved if a moderate fraction of the commodity demand is procured via spot markets. The results also show that companies who use spot markets can offer a higher expected service level, but that they might experience a higher variability in profits than companies who do not use spot markets. We illustrate our analytical results with numerical examples throughout the paper.     

Risk minimizing hedging for a partially observed high frequency data model

Risk-minimizing hedging strategies for contingent claims are studied in a general model for intraday stock price movements in the case of partial information. The dynamics of the risky asset price is described throught a marked point process Y, whose local characteristics depend on some unobservable hidden state variable X. In the model presented the processes Y and X may have common jump times, which means that the trading activity may affect the law of X and could be also related to the presence of catastrophic events. The hedger is restricted to observing past asset prices. Thus, we are in presence not only of an incomplete market situation but also of partial information. Considering the case where the price of the risky asset is modeled directly under a martingale measure, the computation of the risk-minimizing hedging strategy under this partial information is obtained by using a projection result (M. Schweizer, Risk minimizing hedging strategies under restricted information, Mathematical Finance 4 (1994) 327–342). This approach leads to a filtering problem with marked point process observations whose solution, obtained via the Kushner-Stratonovich equation, allows us to provide a complete solution to the heding problem.     

基于Tsallis理论的中国股市收益分布研究

应用Tsallis提出的非广延统计力学理论以及与之密切相关的非线性Fokker-Planck方程所描述的动力系统,根据我国上证指数和深证指数2004年1月1日～2008年11月13日的高频数据,分析了在三种不同的时间标度下股指收益的概率分布,发现Tsallis分布可以很好地描述两市收益分布的尖峰厚尾有限方差等特征,同时也给出了市场微观动力学层面的解释。揭示出我国上海和深圳股市的价格过程并不符合随机游走,而是反常扩散过程,两市具有十分接近的非线性动力系统特征。所得结论对于研究我国金融市场的资产配置和定价、风险管理和制度建设都具有重要的意义。     

On the performance of West’s bubble test: A simulation approach

In this research we examine the ability of West’s bubble test [1] in detecting speculative bubbles using Brock’s (1982) [2] intertemporal general equilibrium model of asset pricing as the basis for a simulation study. In this setting, (1) the economy, by construction is efficient and produces the maximally possible amount of welfare for society, and (2) asset prices reflect the utility-maximizing behavior of consumers and the profit-maximizing behavior of firms. We find that the West’s bubble test flag as “bubbles” in the simulated data yet the data is produced from an economy in which markets are efficient in welfare production.