Financial Market Model Research Articles

Creation and Valuation of Instruments Compensating Lower Share Prices with the Help of Black–Scholes Formula

Abstract In this paper, we present a 1-period model of the Polish financial market from the view point of KGHM, the Polish largest listed company that suffered huge declines in share prices from 125 PLN in August 2015 to 60 PLN in January 2015. Our goal is to show how KGHM might create a portfolio (with practically zero cost), which would fully compensate the abovementioned declines. The methodology presented below may be equally well employed by many other listed companies and investment funds, as well. We create here a matrix model of the Polish financial market and employ the Black-Scholes formula to valuate portfolios compensating potential declines of KGHM’s shares prices. To give more insight to practitioners wishing to apply the results presented here to other listed companies, we distinguish two cases. In one of them, volatility of KGHM’s share prices is 20%, and in the other case it equals 33%.

Herding behaviour and volatility clustering in financial markets

We propose a financial market model in which speculators follow a linear mix of technical and fundamental trading rules to determine their orders. Volatility clustering arises in our model due to speculators’ herding behaviour. In case of heightened uncertainty, speculators observe other speculators’ actions more closely. Since speculators’ trading behaviour then becomes less heterogeneous, the market maker faces a less balanced excess demand and consequently adjusts prices more strongly. Estimating our model using the method of simulated moments reveals that it is able to explain a number of stylized facts of financial markets quite well. Various robustness checks with respect to the model setup reveal that our results are quite stable.

ON THE NUMERICAL ASPECTS OF OPTIMAL OPTION HEDGING WITH TRANSACTION COSTS

We present a numerical study of non-self-financing hedging of European options under proportional transaction costs. We describe an algorithmic approach based on a discrete time financial market model that extends the classical binomial model. We review the analytical basis for our algorithm and present a variety of empirical results using real market data. The performance of the algorithm is evaluated by comparing to a Black–Scholes delta hedge with transaction costs incorporated. We also evaluate the impact of recalibrating the hedging strategy one or more times during the life of the option using the most recent market data. These results are compared to a recalibrated Black–Scholes delta hedge modified for transaction costs.

Bitcoin Market Volatility Analysis Using Grand Canonical Minority Game

In this paper we propose to use the Grand Canonical Minority Game (GCMG, a highly simplified financial market model) as a model of bitcoin market to show how the lack of an income for “miners”, similar to yield earned by bond holders, could be a structural reason for high volatility of bitcoin price in a reference currency. Coherently with present analysis, the introduction of future contracts on bitcoin would have the effect of reducing the overall market volatility.

A GENERAL ORNSTEIN–UHLENBECK STOCHASTIC VOLATILITY MODEL WITH LÉVY JUMPS

We present a general class of stochastic volatility models with jumps where the stochastic variance process follows a Lévy-driven Ornstein–Uhlenbeck (OU) process and the jumps in the log-price process follow a Lévy process. This financial market model is a true extension of the Barndorff-Nielsen–Shephard (BNS) model class and can establish a weak link between log-price jumps and volatility jumps. Furthermore, we investigate the weak-link [Formula: see text]-OU-BNS model as a special case, where we calculate the characteristic function of the logarithmic price in closed form. The classical [Formula: see text]-OU-BNS model can be obtained as a limit of weak-link [Formula: see text]-OU-BNS models in the Skorokhod topology. We highlight that the weak-link property may be a useful model extension in the case of pricing barrier options.

Application of the Nonlinear Oscillations Theory to the Study of Non-equilibrium Financial Market

The research deals with the construction, implementation and analysis of the model of the non-equilibrium financial market using econophysical approach and the theory of nonlinear oscillations. We used the scaled variation of supply and demand prices and elasticity of these two variables as dynamic variables in the simulation of the non-equilibrium financial market. View of the dynamic variables data was determined based on the strength of econophysical prerequisites using the model of hydrodynamic type. As a result, we found that the non-equilibrium market can be described with a good degree of accuracy with oscillator models with nonlinear rigidity and a self-oscillating system with inertial self-excitation. The most important states of model of oscillation non-equilibrium model of the market were found, including the appearance of chaos and its mechanisms. We have made the calculations of the correlation dimension for the financial time series. The results show that all observed time series have a clearly defined chaotic dynamic nature.

Models of Financial Markets

Computer-based algorithms & models have become important in trading in financial markets. We illustrate the significance of model analysis of financial systems by a case study of BlackRock’s analytical platform called ‘Aladdin’. The nature of the model used in a computer algorithm is central to its real performance. Unreal models in financial algorithms will yield inaccurate performances. We review five fundamental models of economic dynamics: (1) traditional price-equilibrium of a commodity market, (2) Keynes-Minsky financial transactions over time, (3) price-disequilibrium of a financial market, (4) investment bank market disequilibrium process, and (5) disequilibrium financial grid of international capital flows. Empirically-valid graphic models are necessary – in order to methodologically develop societal-useful normative economic theory -- based upon the real natural-experiments of societies in economic history.

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 of domestic investors in the interpretation of home public signals affect 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.Received January 15, 2011; editorial decision May 16, 2016 by Editor Geert Bekaert.

A Heterogeneous-Agent Foundation of the Representative-Agent Approach

The representative-agent approach is widely used in consumption-based asset pricing. From a theoretical point of view, quite restrictive assumptions on the underlying economy are needed for asset prices to depend only on aggregate consumption. A heterogeneous-agent financial market model is presented with all investors following simple rebalancing rules where aggregation already fails. A meaningful specification of a representative agent is still possible: Instead of asset prices per se the representative agent indicates the direction in which relative asset prices tend to in expectation from one time period to the next. The objective function of the representative agent is independent of the set of rebalancing rules participating in the market.

Piecewise-Linear Maps and Their Application to Financial Markets

The goal of this paper is to review some work on agent-based financial market models in which the dynamics is driven by piecewise-linear maps. As we will see, such models allow deep analytical insights into the functioning of financial markets, may give rise to unexpected dynamics effects, allow explaining a number of important stylized facts of financial markets, and offer novel policy recommendations. However, much remains to be done in this rather new research field. We hope that our paper attracts more scientists to this area.

Volatility clustering: A nonlinear theoretical approach

This paper verifies the endogenous mechanism and economic intuition on volatility clustering using the coexistence of two locally stable attractors proposed by Gaunersdorfer et al. (2008). By considering a simple asset pricing model with two types of boundedly rational traders, fundamentalists and trend followers, and noise traders, we provide theoretical conditions on the coexistence of a locally stable steady state and a locally stable invariant circle of the underlying nonlinear deterministic financial market model and show numerically that the interaction of the coexistence of the deterministic dynamics and noise processes can endogenously generate volatility clustering and long range dependence in volatility observed in financial markets. Economically, volatility clustering occurs when neither the fundamental nor trend following traders dominate the market and when traders switch more often between the two strategies.

The Federal Reserve's Tools for Policy Normalization in a Preferred Habitat Model of Financial Markets

We develop a model to analyze monetary policy implementation with multiple Federal Reserve liabilities and superabundant reserves. The analysis demonstrates the Federal Reserve's tools including interest on excess reserves (IOER), overnight reverse repurchase agreements (ON RRP), and term deposits should allow the Federal Reserve to raise the short‐term interest rates to any desired level. We find the contribution of each the increase in the IOER and ON RRP offering rates in firming money market rates suggested by the data during the December 2015 policy tightening event is remarkably similar to the effect of each tool implied by the calibrated model.

Volatility Clustering: A Nonlinear Theoretical Approach

This paper verifies the endogenous mechanism and economic intuition on volatility clustering using the coexistence of two locally stable attractors proposed by Gaunersdorfer, Hommes and Wagener (2008). By considering a simple asset pricing model with two types of boundedly rational traders, fundamentalists and trend followers, and noise traders, we provide conditions on the coexistence of locally stable steady state and invariant cycle of the underlying nonlinear deterministic financial market model and show numerically that the interaction of the coexistence of the deterministic dynamics and noise processes can endogenously generate volatility clustering and long range dependence in volatility observed in financial markets. Economically, volatility clustering occurs when neither the fundamental nor trend following traders dominate the market and when traders switch more often between the two strategies.

A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework

In this paper, we review pricing of the variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework and review the existing numerical methods. We also discuss pricing under the complete/incomplete financial market models, stochastic mortality and optimal/sub-optimal policyholder behavior, and in the presence of taxes. For numerical valuation of these contracts in the case of simple risky asset process, we develop a direct integration method based on the Gauss-Hermite quadratures with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is easier to implement and faster when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a numerical benchmark for practitioners and researchers developing pricing of variable annuity guarantees to assess the accuracy of their numerical implementation.

Bankruptcy prevention in multiperiod Markowitz optimization problem

A multiperiod version of the Markowitz optimization problem is considered by assuming that the financial market model is discrete with respect to time and the number of scenarios. Basing on the optimal strategy of securities trading, we find the upper bound of the expected final portfolio value which does not lead to bankruptcy.

Existence of solutions in non-convex dynamic programming and optimal investment

We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization in finite discrete time without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal investment strategies for non-concave utility maximization problems in financial market models with frictions, a first result of its kind. The proofs are based on the dynamic programming principle whose validity is established under quite general assumptions.

Polynomial diffusions and applications in finance

This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility, commodities and electricity. Uniqueness of polynomial diffusions is established via moment determinacy in combination with pathwise uniqueness. Existence boils down to a stochastic invariance problem that we solve for semialgebraic state spaces. Examples include the unit ball, the product of the unit cube and nonnegative orthant, and the unit simplex.

Adverse effects of leverage and short-selling constraints in a financial market model with heterogeneous agents

This paper investigates the impact of leverage and short-selling constraints on financial market stability. Investors׳ demand is modelled in a well-known asset pricing model with heterogeneous beliefs. In particular, I generalise the heterogeneous agents model of Brock and Hommes (1998) and Anufriev and Tuinstra (2013) to allow for leverage constraints as well as a short-selling tax. I consider two examples of adaptive belief systems describing the coevolution of prices and investors׳ beliefs. First, if the market is inhabited by fundamentalist and chartist traders, demand constraints have potential adverse effects and may restrict the stabilising fundamentalist strategy such that mispricing and price volatility increase. Second, if the market is inhabited by fundamentalists, optimists and pessimists with fixed beliefs, demand constraints drive down price volatility, but mispricing remains. The results suggest the stabilising effects of demand constraints in financial markets are limited. Only if asset prices are too high compared to fundamentals, policy makers should consider constraining leverage ratios in order to deflate financial bubbles.

Toward a General Model of Financial Markets

This paper aims to discuss the possibilities of capturing efficient market hypothesis and behavioral finance under a general framework using the literature of decision theories and information sciences. The focus is centered on the broad definition of rationality, the imprecision and reliability of information. The main thesis advanced is that the root of behavioral anomalies comes from the imprecision and reliability of information. Modeling on basis of imprecision and reliability of information within the broad definition of rationality will lead us to a more general model of financial markets.

Risk-Taking in Contests: The Impact of Fund-Manager Compensation on Investor Welfare

We provide a tractable model of competition in rank-order contests with general prize structures. A leading example of such a situation is the competition between fund managers whose compensation depends on how well they performed relative to their peers. We analyze their trading behavior In a dynamic financial market model a la Black Scholes. In the unique symmetric equilibrium, fund managers use randomized trading strategies which endogenously create risk. This risk is unrelated to the uncertainty generated by the assets traded in the underlying financial market. Furthermore, this risk is excessive as there exists a trading strategy that dominates the equilibrium return distribution in the sense of second-order stochastic dominance. This trading strategy takes the form of a simple index strategy. Excessive risk-taking of fund managers leads to welfare losses if investors are risk-averse. Numerical examples indicate that welfare losses are substantial. Finally, we show that fund managers use more risky strategies, in the sense of second-order stochastic dominance, when competition between the agents increases.