Financial Market Model Research Articles

A Financial Market Model for the US and the Netherlands

This paper describes a capital market model for the Netherlands. This capital market model can be used to evaluate the pension agreement between the government, employers and employees in the Netherlands. Pension funds may invest in a stock market index and in bond funds which rebalance permanently their portfolio to fix the maturity. So we need a description of the stock market and the bond market inclusive the term structure. Both the nominal bonds as well as the development of the stock returns depend on the inflation process which needs to be modelled, too. Net benefits of pensions can be considered as a derivative of bonds and equity, because both the benefits and premiums depend on the investment results. So we need an instrument to evaluate derivative products. The Koijen et al. (2010) model meets all these requirements and will be used after reestimation using Dutch data.This paper provides a technical documentation of this capital market model and details on the derivations and the estimation. The estimation results are compared to estimates for the US. The results for the Netherlands deviate in several respects from those for the US. In particular, the estimates are less signi cant. A possible explanation may be that (not included) exchange rate fluctuations are more relevant for Europe than for the US.Due to the small open economy character and the data construction this model can be considered as a model for the north European capital market.This estimated capital market model will be used to construct scenario sets. These scenarios will be used in an asset liability model (ALM) to evaluate the pension agreement.The Koijen et al. (2010) model is related to Brennan and Xia (2002), Campbell and Viceira (2001) and Sangvinatsos and Wachter (2005). More details of the model can be found in Koijen et al. (2005) and Koijen et al. (2006). A survey of all risks that pension funds are facing, can be found in Broer (2010).Section 2 presents the model assumptions. The link between nominal and inflation linked bonds is discussed in section 3, just as the term structure. Bond funds implementing constant duration are the subject of section 4. The model is formulated in continuous time, but for simulation and estimation purposes a discretized version is necessary. This discretization is discussed in section 5. To determine the value of derivative products, as for instance pension rights, risk-neutral simulation is used which is discussed in section 6. The data used to estimate the model are discussed in section 7. Section 8 presents the estimation procedure and section 9 the estimation results. The model will be used to generate scenarios. Section 10 presents some possible scenarios to get some feeling for the results. Section 11 concludes.

Russia’s Financial System: Stimulation of Innovative Growth, Increasing Role in Global Financial Markets

This paper offers proposals on stimulation of Russia's innovative economic growth through share ownership diversification, improving corporate governance practice and capital structure transformation. The paper also contains concepts on how to strengthen Russia’s role in global financial markets through development of financial, monetary, investment, innovation policy and transformation of financial market model.

ROBUST MEAN-VARIANCE HEDGING AND PRICING OF CONTINGENT CLAIMS IN A ONE PERIOD MODEL

In this paper, we consider the mean-variance hedging problem of contingent claims in a financial market model composed of assets with uncertain price parameters. We consider the worst case of model parameters required to solve the minimax problem. In general, such minimax problems cannot be changed to maximin problems. The main approach we develop is the randomization of the parameters, which allows us to change minimax to maximin problems, which are easier to solve. We provide an explicit solution for the robust mean-variance hedging problem in the single-period model for some types of contingent claims.

Structural stochastic volatility in asset pricing dynamics: Estimation and model contest

In the framework of small-scale agent-based financial market models, the paper starts out from the concept of structural stochastic volatility, which derives from different noise levels in the demand of fundamentalists and chartists and the time-varying market shares of the two groups. It advances several different specifications of the endogenous switching between the trading strategies and then estimates these models by the method of simulated moments (MSMs), where the choice of the moments reflects the basic stylized facts of the daily returns of a stock market index. In addition to the standard version of MSM with a quadratic loss function, we also take into account how often a great number of Monte Carlo simulation runs happen to yield moments that are all contained within their empirical confidence intervals. The model contest along these lines reveals a strong role for a (tamed) herding component. The quantitative performance of the winner model is so good that it may provide a standard for future research.

Biased trader model and analysis of financial market dynamics

This study focuses on various trader behaviors that affect market dynamics. In particular, the effects of a covering mechanism, learning mechanism and bias mechanism are analyzed through agent-based financial market model. An XCS classifier system is used to model trader learning mechanism. A trader model is proposed to formulate a trader decision model that combines bias mechanisms with learning mechanisms. The results reveal that biased traders survive under evolving markets and affect price dynamics. The model contributes to understanding the market behavior and potential sources of deviation from efficient market equilibrium.

Market viability via absence of arbitrage of the first kind

It is shown that, in a semimartingale financial market model, there is equivalence between absence of arbitrage of the first kind (a weak viability condition) and the existence of a strictly positive process that acts as a local martingale deflator on nonnegative wealth processes.

The endogenous dynamics of financial markets: Interaction and information dissemination

We investigate the process that different interactions between investors will prompt information to propagate along a differentiated path and construct a financial market model. As information spreads, increasingly investors are attracted to participate in trading, then the “herding effect” is magnified gradually, which will induce the topology of market network to change and the price to fluctuate. Especially, under different initial conditions or parameters, the peak and fat-tail property is produced and the obtained statistic values coincide with empirical results: the power-law exponents between the peak value of return probability distribution and the time scales range from 0.579 to 0.747, and the exponents between the accumulation distribution and the return on the tail are close to 3. Besides, the extent of volatility clustering in our produced price series is close to that of S&P 500 and locates between NASDAQ and HSI. All the results obtained here indicate that the continuous variation of the “herding effect” resulting from information propagation among interacting investors may be the origin of stylized facts of price fluctuations.

MULTIPLICATIVE APPROXIMATION OF WEALTH PROCESSES INVOLVING NO‐SHORT‐SALES STRATEGIES VIA SIMPLE TRADING

A financial market model with general semimartingale asset–price processes and where agents can only trade using no‐short‐sales strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy‐and‐hold trading. This approximation is based on controlling the proportions of wealth invested in the assets. As an application, the utility maximization problem is considered and it is shown that optimal expected utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy‐and‐hold strategies.

On Certain Analogies Between the Laws of Quantum Mechanics and Rules of an English Auction

On Certain Analogies Between the Laws of Quantum Mechanics and Rules of an English Auction It is a self-evident truth that nowadays a growing number of economic phenomena is described by means of physics methods. The most frequent theories derived from physics and applied to economy are: (1) the universal gravitation law and (2) the first as well as the second law of thermodynamics. The methods of static physics are applicable also to the theory of financial markets. In this case it is assumed that the financial market is composed of single participants interacting as a system of particles. Such approach is associated with a model of financial market otherwise known as a minority game. It is postulated that the process of securities and money allocation is performed on the basis of prices fluctuation, where - if a vast majority of investors tend to purchase goods or services - the sale constitutes a more profitable option, and vice versa. The players who end up on minority side win. At the end of the XX century the economy commenced to apply the laws of quantum mechanics. These laws proved to be useful, in particular when attempting to generalize game theory, which resulted in quantum games. The aim of the paper is to compare the rules and auction mechanisms with selected laws of quantum mechanics. This paper aims also to introduce the basic concepts of quantum mechanics to the process of economic phenomena modeling. Quantum mechanics is a theory describing a behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties. The key role in quantum mechanics is played by: (1) the Schrödinger equation describing the probability amplitude for the particle to be found at a given position and at a given time, as well as (2) the Heisenberg uncertainty principle stating that a certain pair of physical properties may not be simultaneously measured to arbitrarily high precision.

Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset

This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study of local stability of the wealth dynamics through the application of recent results on the linearization and stability of random dynamical systems (Evstigneev et al. Proc Am Math Soc 139:1061–1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary stability. A locally evolutionarily stable investment strategy in the evolutionary model with a risk-free asset is derived, extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial dynamic models involving randomness.

Heterogeneous Speculators and Asset Price Dynamics: Further Results from a One-Dimensional Discontinuous Piecewise-Linear Map

In this paper we continue exploring a recently introduced financial market model in which boundedly rational agents follow technical and fundamental trading rules to determine their orders. Amongst other things, our model reveals that interactions between heterogeneous speculators can generate interesting boom-bust cycles. In addition, we provide an extensive analytical treatment of the model's underlying dynamical system, which is given by a one-dimensional discontinuous piecewise-linear map. One result is that we detect a period-adding bifurcation sequence, implying the existence of infinitely many stable cycles. Moreover, we analytically determine the parameter space that yields stable, cyclical and chaotic asset price fluctuations.

On the semimartingale property of discounted asset-price processes

A financial market model where agents trade using realistic combinations of simple (i.e., finite combinations of buy-and-hold) no-short-sales strategies is considered. Minimal assumptions are made on the discounted asset-price process — in particular, the semimartingale property is not assumed. Via a natural market viability assumption, namely, absence of arbitrage of the first kind, we establish that discounted asset-prices have to be semimartingales. Our main result can also be regarded as reminiscent of the Fundamental Theorem of Asset Pricing.

On derivatives with illiquid underlying and market manipulation

In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework to construct optimal trading strategies under market impact in a multi-player framework by introducing strategic interactions into the model of Almgren [Appl. Math. Finance, 2003, 10(1), 1–18]. Specifically, we consider a financial market model with several strategically interacting players who hold European contingent claims and whose trading decisions have an impact on the price evolution of the underlying. We establish the existence and uniqueness of equilibrium results for risk-neutral and CARA investors and show that the equilibrium dynamics can be characterized in terms of a coupled system of possibly nonlinear PDEs. For the linear cost function used by Almgren, we obtain a (semi) closed-form solution. Analysing this solution, we show how market manipulation can be reduced.

The near-extreme density of intraday log-returns

The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge amount of records to obtain significant statistics, and thus limiting its practical applications. Focussing, instead, on the closely related density of “near-extremes”–the distance between a record and the maximal value–can render the statistical methods to be more suitable in the practical applications and/or validations of models. We apply this recently proposed method in the empirical validation of an adapted financial market model of the intraday market fluctuations.

Utility maximization in markets with bid–ask spreads

A one-period financial market model with transaction costs is considered in this paper. Redefining the risky asset price process in a suitable way, we obtain an explicit solution to the utility maximization problem when the risk preferences of the investor are based on the exponential utility function and a liability can be included in her portfolio. The arbitrage-free interval price for a general liability, as well as its replication price, is characterized in terms of expectations with respect to equivalent martingale measures. The indifference price is derived and its asymptotic limit when the risk aversion is going to infinity is analysed.

Local Stability Analysis of a Stochastic Evolutionary Financial Market Model with a Risk-free Asset

This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study of local stability of the wealth dynamics through the application of recent results on the linearization and stability of random dynamical systems (Evstigneev, Pirogov and Schenk-Hoppe, Proceedings of the American Mathematical Society 139, 1061-1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary stability. A locally evolutionarily stable investment strategy in the evolutionary model with a risk-free asset is derived, extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial dynamic models involving randomness.

Classical and Quantum Physics in Selected Economic Models

Classical and Quantum Physics in Selected Economic ModelsA growing number of economic phenomena are nowadays described with methods known in physics. The most frequently applied physical theories by economists are: (1) the universal gravitation law and (2) the first and second law of thermodynamics. Physical principles can also be applied to the theory of financial markets. Financial markets are composed of individual participants who may be seen to interact as particles in a physical system. This approach proposes a financial market model known as a minority game model in which securities and money are allocated on the basis of price fluctuations, and where selling is best option when the vast majority of investors tend to purchase goods or services, and vice versa. The players who end up being on the minority side win.The above applications of physical methods in economics are deeply rooted in classical physics. However, this paper aims to introduce the basic concepts of quantum mechanics to the process of economic phenomena modelling. Quantum mechanics is a theory describing the behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties. The key role in quantum mechanics is played by: (1) the Schrödinger equation describing the probability amplitude for the particle to be found in a given position and at a given time, and as (2) the Heisenberg uncertainty principle stating that certain pairs of physical properties cannot be economic applications of the Schrödinger equation as well as the Heisenberg uncertainty principle. We also try to describe the English auction by means the quantum mechanics methods.

Explanation of Investment Instruments Return Distribution Deviation from Normality - According to Dynamic Financial Market Model (Brief Version)

Explanation of Investment Instruments Return Distribution Deviation from Normality - According to Dynamic Financial Market Model (Brief Version)

Differences of Opinion and International Equity Markets

We develop an international financial market model in which domestic and foreign residents differ in their beliefs about the information content in public signals. We determine how informational advantages by domestic (foreign) investors in the interpretation of home (foreign) public signals impact equity markets. Our model generates four standard international pricing anomalies: (i) the co-movement of returns and international capital flows; (ii) home equity preference; (iii) the dependence of firm returns on home and foreign factors; and (iv) abnormal returns around foreign firm cross-listing in the home market.

Differences of Opinion and International Equity Markets

We develop an international financial market model in which domestic and foreign residents differ in their beliefs about the information content in public signals.We determine how informational advantages by domestic investors in the interpretation of home public signals impact equity markets. We evaluate the ability of our model to generate four international finance anomalies: (i) the co-movement of returns and capital flows; (ii) home-equity preference; (iii) the dependence of firm returns on home and foreign factors; and (iv)abnormal returns around foreign firm cross-listing in the home market.Their relationships with empirical differences-of-opinion proxies are consistent with the model.