Information-based multi-assets artificial stock market with heterogeneous agents

In this paper, an artificial stock market characterized by heterogeneous and informed agents is presented. The heterogeneous agents are seen as nodes of sparsely connected graphs. The agents trade risky assets and are characterized by sentiments, amount of cash and stocks owned. Agents share information and sentiments by means of interactions determined by graphs. A central market maker (clearing house mechanism) determines the price processes for each stock at the intersection of the demand and supply curves. In this framework, the statistical properties of the univariate and multivariate process of prices and returns are studied. Importantly, concerning univariate price processes, the proposed model is able to reproduce unit root, volatility cluster and fat tails of returns. The multivariate price process exhibits both static and dynamic stylized facts, in particular the presence of static factors and common trends. Static factors are studied making reference to the cross-correlation between returns of different stocks, whereas the common trends are investigated considering the variance–covariance matrix of prices. The proposed approach allows to endogenously reproduce the multivariate stylized facts.     

On hedging in finite security markets

A market is considered where trading can take place only at discrete time points, the trading frequency cannot grow without bound, and the number of states of nature is finite. The main objectives of the paper are to show that the market can be completed also with highly correlated risky assets, and to describe an efficient algorithm to compute a self-financing hedging strategy. The algorithm consists off-line of a backwards recursion and on-line of the solution, in each period, of a system of linear equations; it is a consequence of a proof where, using a well-known mathematical property, it is shown that uniqueness of the martingale measure implies completeness also in our setting. The significance of ‘multistate’ models versus the familiar binomial model is discussed and it is shown how the evolution of prices of the (correlated) risky assets can be chosen so that a given probability measure is already the unique equivalent martingale measure.     

MARKET FORCES AND DYNAMIC ASSET PRICING

We study a dynamic model of asset pricing which is driven by two characteristic market features: the law of investor demand (e.g., “buy low, sell high”) and the law of the market institution (which codifies the trading rules under which the market operates). We demonstrate in a simple investor–specialist trading market that these features are sufficient to guarantee an equilibrium where investors' trading strategies and the specialist's rule of price adjustments are best responses to each other. The drift term appearing in the resulting equation of the asset price process may be interpreted using Newtonian mechanics as the acceleration of a “market force.” If either of the market participants is risk-neutral, the result leads to risk-neutral asset pricing (e.g., the Black and Scholes option pricing formula).     

Rebalancing Multiple Assets with Mutual Price Impact

We find asymptotically optimal trading policies for long-term investors with constant relative risk aversion, in a multiple-assets market, where expected returns and covariances are constant, and the execution price of each asset is linear in the trading intensities of all assets. Trading toward the frictionless target is optimal, when the current portfolio differs from the target by a principal portfolio—an eigenvector of the inverse impact matrix times the covariance matrix. Optimal policies approach the frictionless target along nonlinear, power-shaped paths, trading faster in more liquid directions, while tolerating wider oscillations along less liquid directions.     

The role of index bonds in universal currency hedging

This study examines the demand for index bonds and their role in hedging risky asset returns against currency risks in a complete market where equity is not hedged against inflation risk. Avellaneda's uncertain volatility model with non-constant coefficients to describe equity price variation, forward price variation, index bond price variation and rate of inflation, together with Merton's intertemporal portfolio choice model, are utilized to enable an investor to choose an optimal portfolio consisting of equity, nominal bonds and index bonds when the rate of inflation is uncertain. A hedge ratio is universal if investors in different countries hedge against currency risk to the same extent. Three universal hedge ratios (UHRs) are defined with respect to the investor's total demand for index bonds, hedging risky asset returns (i.e. equity and nominal bonds) against currency risk, which are not held for hedging purposes. These UHRs are hedge positions in foreign index bond portfolios, stated as a fraction of the national market portfolio. At equilibrium all the three UHRs are comparable to Black's corrected equilibrium hedging ratio. The Cameron-Martin-Girsanov theorem is applied to show that the Radon-Nikodym derivative given under a P -martingale, the investor's exchange rate (product of the two currencies) is a martingale. Therefore the investors can agree on a common hedging strategy to trade exchange rate risk irrespective of investor nationality. This makes the choice of the measurement currency irrelevant and the hedge ratio universal without affecting their values.     

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.     

Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases

In a financial market with one riskless asset and n risky assets whose prices are lognormal, we solve in a closed form the problem of a pension fund maximizing the expected CRRA utility of its surplus till the (stochastic) death time of a representative agent. We consider a unique asset allocation problem for both accumulation and decumulation phases. The optimal investment in the risky assets must decrease during the first phase and increase during the second one. We accordingly suggest it is not optimal to manage the two phases separately, and outsourcing of allocation decisions should be avoided in both phases. JEL: G23, G11 MSC 2000: 62P05, 91B28, 91B30, 91B70, 93E20     

Option pricing for large agents

This paper considers arbitrage-free option pricing in the presence of large agents. These large agents have a significant market power, and their trading strategies influence the dynamics of the financial asset prices. First, a simple asset pricing model in the presence of large agents is presented. Then a nonlinear partial differential equation is found for the prices of European options in the model. The unit option price depends on the large agent's asset holdings. Finally, a game model is introduced for the interaction between different market players. In this game, the outstanding number of options, as well as the option price, is found as a Nash equilibrium.     

Optimal portfolio choice and stochastic volatility

In this paper we examine the effect of stochastic volatility on optimal portfolio choice in both partial and general equilibrium settings. In a partial equilibrium setting we derive an analog of the classic Samuelson–Merton optimal portfolio result and define volatility‐adjusted risk aversion as the effective risk aversion of an individual investing in an asset with stochastic volatility. We extend prior research which shows that effective risk aversion is greater with stochastic volatility than without for investors without wealth effects by providing further comparative static results on changes in effective risk aversion due to changes in the distribution of volatility. We demonstrate that effective risk aversion is increasing in the constant absolute risk aversion and the variance of the volatility distribution for investors without wealth effects. We further show that for these investors a first‐order stochastic dominant shift in the volatility distribution does not necessarily increase effective risk aversion, whereas a second‐order stochastic dominant shift in the volatility does increase effective risk aversion. Finally, we examine the effect of stochastic volatility on equilibrium asset prices. We derive an explicit capital asset pricing relationship that illustrates how stochastic volatility alters equilibrium asset prices in a setting with multiple risky assets, where returns have a market factor and asset‐specific random components and multiple investor types. Copyright © 2011 John Wiley & Sons, Ltd.     

Projection Pricing

A significant problem in modern finance theory is how to price assets whose payoffs are outside the span of marketed assets. In practice, prices of assets are often assigned by using the capital asset pricing model (CAPM). If the market portfolio is efficient, the price obtained this way is equal to the price of an asset whose payoff, viewed as a vector in a Hilbert space of random variables, is projected orthogonally onto the space of marketed assets. This paper looks at the pricing problem from this projection viewpoint. It is shown that the results of the CAPM formula are duplicated by a formula based on the minimum-norm portfolio, and this pricing formula is valid even in cases when there is no efficient portfolio of risky assets. The relation of the pricing to other aspects of projection are also developed. In particular, a new pricing formula, called the correlation pricing formula, is developed that yields the same price as the CAPM, but is likely to be more accurate and more convenient than the CAPM in some cases.     

Option pricing when asset returns jump interruptedly

This paper proposes an extension of Merton's jump‐diffusion model to reflect the time inhomogeneity caused by changes of market states. The benefit is that it simultaneously captures two salient features in asset returns: heavy tailness and volatility clustering. On the basis of an empirical analysis where jumps are found to happen much more frequently in risky periods than in normal periods, we assume that the Poisson process for driving jumps is governed by a two‐state on‐off Markov chain. This makes jumps happen interruptedly and helps to generate different dynamics under these two states. We provide a full analysis for the proposed model and derive the recursive formulas for the conditional state probabilities of the underlying Markov chain. These analytical results lead to an algorithm that can be implemented to determine the prices of European options under normal and risky states. Numerical examples are given to demonstrate how time inhomogeneity influences return distributions, option prices, and volatility smiles. The contrasting patterns seen in different states indicate the insufficiency of using time‐homogeneous models and justify the use of the proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity

We consider the problem of optimal portfolio choice using the Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR) measures for a market consisting of n risky assets and a riskless asset and where short positions are allowed. When the distribution of returns of risky assets is unknown but the mean return vector and variance/covariance matrix of the risky assets are fixed, we derive the distributionally robust portfolio rules. Then, we address uncertainty (ambiguity) in the mean return vector in addition to distribution ambiguity, and derive the optimal portfolio rules when the uncertainty in the return vector is modeled via an ellipsoidal uncertainty set. In the presence of a riskless asset, the robust CVaR and VaR measures, coupled with a minimum mean return constraint, yield simple, mean-variance efficient optimal portfolio rules. In a market without the riskless asset, we obtain a closed-form portfolio rule that generalizes earlier results, without a minimum mean return restriction.     

Options on constant proportion portfolio insurance with guaranteed minimum equity exposure

In the present paper we study a new exotic option offering participation in a dynamic asset allocation strategy, which is an extension of the well‐known Constant Proportion Portfolio Insurance (CPPI) strategy. Our novel approach consists in assuming that the percentage of wealth invested in stocks cannot go under a fixed level, called guaranteed minimum equity exposure (GMEE). In particular, our proposal ensures to overcome the so‐called cash‐in risk, typically related to a standard CPPI technique, simultaneously guaranteeing the equity market participation. We look deeper into the valuation of call and put options linked to this new CPPI‐GMEE strategy. A particular attention is devoted to the analysis of key parameters' value as to gain a better understanding of the sensitivities of the option prices, when changing, for example, the embedded guarantee level. To show the effectiveness of our proposal we provide a detailed computational analysis within the Heston‐Vasicek framework, numerically comparing the evaluation of the price of European plain vanilla options when the underlying is either a purely risky asset, a standard CPPI portfolio and a CPPI with GMEE.     

Variational Formulation of a General Equilibrium Model with Incomplete Financial Markets and Numeraire Assets: Existence

We present a general equilibrium model with incomplete financial markets and numeraire assets. We assume that there are 2 periods of time, say today and tomorrow. In period 0, households exchange goods and assets and then consumption takes place; in period 1, one of S possible states of nature occurs. In each of them, assets pay their returns, which are measured in units of a given physical good, i.e., the numeraire commodity; households exchange goods; finally, consumption takes place. We define a consumption, portfolio holding, commodity and asset price vector as an equilibrium vector associated with a given economy, if at those prices and economies households maximize, and market clears. While the existence proof by Geneakoplos and Polemarchakis (Essays in honor of K.J. Arrow, vol 3, Cambridge University Press, Cambridge, pp 65–95, 1986) uses a fixed point argument, we provide an independent existence result in terms of variational inequalities. That approach allows us to get the desired existence result under some different and more general or realistic assumptions than those usually made in the literature.     

国际铜期货市场整合：沪铜国际影响凸显

本文运用含协整残差的双变量EGARCH模型,研究上海SHFE和伦敦LME铜期货市场的动态整合关系.统计结果显示两个市场的收益及其风险存在对称的溢出效应,全球铜市供求因素驱动最新收益和风险信息在两者之间传递。沪铜期货有突出的国际定价影响.在全球24小时交易中,LME和SHFE交替成为国际铜价的主要信息来源.SHFE和LME市场的收益变化均以对方市场的影响为主;市场风险则以本市场的影响为主.影响两个市场动态整合度的因素有滞后一期的市场风险、沪铜成交量、伦铜的超额收益等。     

Optimal portfolios of a small investor in a limit order market: a shadow price approach

We study Merton’s portfolio optimization problem in a limit order market. An investor trading in a limit order market has the choice between market orders that allow immediate transactions and limit orders that trade at more favorable prices but are executed only when another market participant places a corresponding market order. Assuming Poisson arrivals of market orders from other traders we use a shadow price approach, similar to Kallsen and Muhle-Karbe (Ann Appl Probab, forthcoming) for models with proportional transaction costs, to show that the optimal strategy consists of using market orders to keep the proportion of wealth invested in the risky asset within certain boundaries, similar to the result for proportional transaction costs, while within these boundaries limit orders are used to profit from the bid–ask spread. Although the given best-bid and best-ask price processes are geometric Brownian motions the resulting shadow price process possesses jumps.     

Estimation of asset demands by heterogeneous agents

We develop optimization models to analyze the demand for financial assets by heterogeneous agents. The models extend Frankel's [J. Portfolio Manage. 11 (4) (1985) 18] earlier approach, and relax the assumption of normality of asset returns. Instead, we assume that investors maximize an expected utility of terminal wealth based on heterogeneous attitudes toward risk. Solving a bi-level optimization program, we endogenously estimate the risk aversion parameters and derive the optimal asset holdings for each agent. The models are tested on United States market data, explaining the market structure better than previously postulated models.     

Optimizing the equity-bond-annuity portfolio in retirement: The impact of uncertain health expenses

This paper derives optimal equity-bond-annuity portfolios for retired households who face stochastic capital market returns, differential exposures to mortality risk and uncertain uninsured health expenses, and differential Social Security and defined benefit pension coverage. The results show that the health spending risk drives household portfolios to shift from risky equities to safer assets and enhances the demand for annuities due to their increasing-with-age superiority over bonds in hedging against life-contingent health spending and longevity risks. Households with higher income have a greater incremental demand for life annuities. The annuities in turn provide greater leverage for equity investment in the remaining asset portfolios.     

Asset pricing and portfolio selection based on the multivariate extended skew-Student-<Emphasis Type="Italic">t</Emphasis> distribution

The returns on most financial assets exhibit kurtosis and many also have probability distributions that possess skewness as well. In this paper a general multivariate model for the probability distribution of assets returns, which incorporates both kurtosis and skewness, is described. It is based on the multivariate extended skew-Student-t distribution. Salient features of the distribution are described and these are applied to the task of asset pricing. The paper shows that the market model is non-linear in general and that the sensitivity of asset returns to return on the market portfolio is not the same as the conventional beta, although this measure does arise in special cases. It is shown that the variance of asset returns is time varying and depends on the squared deviation of market portfolio return from its location parameter. The first order conditions for portfolio selection are described. Expected utility maximisers will select portfolios from an efficient surface, which is an analogue of the familiar mean-variance frontier, and which may be implemented using quadratic programming.