1,721,007 research outputs found
Mathematical Analysis of the Chaotic Behavior in Monetary Policy Games
No full textThis thesis discusses the concept of chaos in monetary policy games. The mathematical framework developed in this thesis addresses two important problems in monetary theory, namely, the time-inconsistency and the complexity in designing, conducting and predicting the impacts of monetary policy on the economy. Considering a noncooperative non-zero-sum differential monetary policy game between the central bank and the public when the coefficients of the system depend on the state and control variables, it is shown that the co-state variables of both players are controllable in all solution concepts. The controllability of the co-state variables means that the monetary policy is time inconsistent even in the open loop Nash game, which is known as a time-consistent policy game in the literature. In other words, the results confirm that the structural time-inconsistency of monetary policy is almost always unavoidable.
To better understand how monetary policy affects the economy, we need to know the response of the public expectations. This can be achieved if the monetary policy behaves in a systematic manner. To this end, this thesis tests the chaotic dynamics of the trajectories of both players. The results reveal that chaotic dynamics is possible in monetary policy games, and it seems that the source of this complexity comes from the chaotic behavior in the public expectations. Chaotic behavior in the strategy of the public sector creates serious difficulties for the policymaker, who wishes to design a policy that controls the business cycles
Mathematical Analysis of the Chaotic Behavior in Monetary Policy Games
No full textThis thesis discusses the concept of chaos in monetary policy games. The mathematical framework developed in this thesis addresses two important problems in monetary theory, namely, the time-inconsistency and the complexity in designing, conducting and predicting the impacts of monetary policy on the economy. Considering a noncooperative non-zero-sum differential monetary policy game between the central bank and the public when the coefficients of the system depend on the state and control variables, it is shown that the co-state variables of both players are controllable in all solution concepts. The controllability of the co-state variables means that the monetary policy is time inconsistent even in the open loop Nash game, which is known as a time-consistent policy game in the literature. In other words, the results confirm that the structural time-inconsistency of monetary policy is almost always unavoidable.
To better understand how monetary policy affects the economy, we need to know the response of the public expectations. This can be achieved if the monetary policy behaves in a systematic manner. To this end, this thesis tests the chaotic dynamics of the trajectories of both players. The results reveal that chaotic dynamics is possible in monetary policy games, and it seems that the source of this complexity comes from the chaotic behavior in the public expectations. Chaotic behavior in the strategy of the public sector creates serious difficulties for the policymaker, who wishes to design a policy that controls the business cycles
Pricing Variance Swaps Under Stochastic Volatility and Stochastic Interest Rate
No full textIn this thesis, we study the issue of pricing discretely-sampled variance swaps under stochastic volatility and stochastic interest rate. In particular, our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, whereas the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR) model. We first extend the framework of [119] by incorporating the CIR interest rate into their Heston model for pricing discretely-sampled variance swaps. We impose partial correlation between the asset price and the volatility, and derive a semi-closed form pricing formula for the fair delivery price of a variance swap. Several numerical examples and comparisons are provided to validate our pricing formula, as well as to show the effect of stochastic interest rate on the pricing of variance swaps.
In addition, the pricing of discretely-sampled variance swaps with full correlation among the asset price, interest rate as well as the
volatility is investigated. This offers a more realistic model with practical importance for pricing and hedging. Since this full correlation model is incompliant with the analytical tractability property, we determine the approximations for the non-affine terms by following the approach in [55] and present a semi-closed form approximation formula for the fair delivery price of a variance swap. Our results confirm that the impact of the correlation between the stock price and the interest rate on variance swaps prices is very crucial. Besides that, the impact of correlation coefficients becomes less apparent as the number of sampling frequencies increases for all cases.
Finally, the issue of pricing discretely-sampled variance swaps under stochastic volatility and stochastic interest rate with regime switching is also discussed. This model is an extension of the corresponding one in [34] and is capable of capturing several macroeconomic issues such as alternating business cycles. Our semi-closed form pricing formula
is proven to achieve almost the same accuracy in far less time compared with the Monte Carlo simulation. Through numerical examples, we discover that prices of variance swaps obtained from the regime switching Heston-CIR model are significantly lower than those of its non-regime switching counterparts. Furthermore, when allowing the Heston-CIR model to switch across three regimes, it is observable that the price of a variance swap is cheapest in the best economy, and most expensive in the worst economy among all
Option Pricing Under the Heston-CIR Model with Stochastic Interest Rates and Transaction Costs
No full textThe celebrated Black-Scholes model on pricing a European option gives a simple and elegant pricing formula for European options with the underlying price following a geometric Brownian motion. In a realistic market with transaction costs, the option pricing problem is known to lead to solving nonlinear partial differential equations even in the simplest model. The nonlinear term in these partial differential equations (PDE) reflects the presence of transaction costs. Leland developed a modified option replicating strategy which depends on the size of transaction costs and the frequency of revision. In this thesis, we consider the problem of option pricing under the Heston-CIR model, which is a combination of the stochastic volatility model discussed in Heston and the stochastic interest rates model driven by Cox-Ingersoll-Ross (CIR) processes with transaction costs. in this case, the reacted nonlinear PDE with respect to the option price does not have a closed-form solution. We use the finite-difference scheme to solve this PDE and conduct model’s performance analysis
Assessing Core Stable Coalitions Based On Social Network Structures
No full textGame theoretic techniques have become deliberate with social network analysis. Studies show that contemporary approach on social network analysis is unable to collectively evaluate the rationality of individuals and synergies that occur between them. Thus, game theory has been selected as an alternate approach for social network analysis to overcome such shortcomings \cite{Narahari}. A field of social network analysis is to examine the strength of ties within a social group and this is referred to as \textit{social cohesion}.
The study of social groups and their tendency to stay in unity is highly correlated to interpersonal relationships and the benefits one can gain to remain in a group \textemdash \ whether it be monetary, popularity, social influence or social needs of an individual \cite{Wei}. Building upon this foundation, we design a type of coalitional game where the social influence rating of members is affected based on the affiliated type of network structure. We first define group cohesion and then assess cohesion on special classes of graphs via the core stability of a coalition. We then study the core stability of a special class of weighted graph followed by the implementation of weighted graphs as a regular expression which can be read by a finite automaton
Assessing Core Stable Coalitions Based On Social Network Structures
No full textGame theoretic techniques have become deliberate with social network analysis. Studies show that contemporary approach on social network analysis is unable to collectively evaluate the rationality of individuals and synergies that occur between them. Thus, game theory has been selected as an alternate approach for social network analysis to overcome such shortcomings \cite{Narahari}. A field of social network analysis is to examine the strength of ties within a social group and this is referred to as \textit{social cohesion}.
The study of social groups and their tendency to stay in unity is highly correlated to interpersonal relationships and the benefits one can gain to remain in a group \textemdash \ whether it be monetary, popularity, social influence or social needs of an individual \cite{Wei}. Building upon this foundation, we design a type of coalitional game where the social influence rating of members is affected based on the affiliated type of network structure. We first define group cohesion and then assess cohesion on special classes of graphs via the core stability of a coalition. We then study the core stability of a special class of weighted graph followed by the implementation of weighted graphs as a regular expression which can be read by a finite automaton
Pricing Volatility Derivatives Under Lévy Processes
No full textIn this thesis, we study the pricing of the volatility derivatives, including VIX options, VIX futures, VXX options and S&P 500 variance futures, under Lévy processes with stochastic volatility. In particular, we investigate the role of different types of jump structures, such as finite-activity jump, infinite-activity jump and double jump structures, as well as the role of variance processes with time-varying mean in the valuation of volatility derivatives. In our models, we assume that the long-term mean of the variance process follows an Ornstein–Uhlenbeck process and specify the infinity-activity jump component of the main process in four cases: the variance gamma process (VG), the normal inverse Gaussian process (NIG), the tempered stable process (TS) and the generalized tempered stable process (GTS). Then, we apply the combined estimation approach of an unscented Kalman filter (UKF) and maximum log-likelihood estimation (MLE) to our models and make an extensive comparison analysis on the performance among the different models.
Our empirical studies reveal three important results. First, the models with infiniteactivity jumps are superior to the models with finite-activity jumps, particularly in pricing VIX options and VXX options. Thus, the infinite-activity jumps cannot be ignored in pricing volatility derivatives. Second, both the infinite-activity jump and diffusion components play important roles in modelling the dynamics of the underlying asset returns for the volatility derivatives. Third, the mean of the variance process for the S&P 500 index returns varies stochastically toward to its long-term mean
Blocking efficiency and competitive equilibria in economies with asymmetric information
No full textIn this thesis, two most fundamental problems in economic theory, namely the existence and the optimality of Walrasian equilibrium, are studied. It is assumed that there is uncertainty about the realized state of nature in an economy and different agents may have different information. Such an economy is called an economy with asymmetric information. Considering a pure exchange symmetric information economy with finitely many states of nature, an atomless measure space of agents and a Banach lattice as the commodity space, it is shown that the private core and the set of Walrasian allocations coincide. The feasibility in this result is taken as free disposal. This optimality is known as the core-Walras equivalence theorem. When the feasibility is defined without free disposal, then it is shown that if a feasible allocation is not in the private core then it is privately blocked by a coalition of any given measure less than that of the grand coalition.
In addition to the above optimality, some other characterizations of Walrasian allocations by the veto power of the grand coalition are also established. One of them deals with robustly efficient allocations in a pure exchange mixed economy with asymmetric information whose commodity space is an ordered separable Banach space having an interior point in its positive cone. Other two characterizations are restricted to a discrete economy with a Banach lattice as the commodity space. First one claims that a feasible allocation is a Walrasian allocation if and only if it is Aubin non-dominated, whereas the other one is interpreted in terms of privately non-dominated allocations in suitable associated economies. The feasibility in all of these results is defined as free disposal.
In a pure exchange asymmetric information economy whose space of agents is a finite measure space, space of states of nature is a probability space with a complete measure, and commodity space is defined as the Euclidean space, the existence of a maximin rational expectations equilibrium is established
Analytic Methods in Finance with Applications to Portfolio and Risk Management
No full textThe thesis studies and develops an investment portfolio strategy using a regular-vine-based forecasting model in period of the recent COVID-19 crisis. The model parameter estimation technique uses families of Bayesian inference and variational Bayes inference. The optimisation model uses family of machine learning algorithms. Overall, the thesis comprises three papers in which the ultimate outcome in paper three is the solution of dynamic portfolio allocation. Prior to that, the first two papers develop the multivariate asset returns forecasting models using the inference function of margins method and then apply it to the third paper in a portfolio optimisation model. The full details of each paper are provided in their abstracts: Chapter 3 for paper one, Chapter 4 for paper two and Chapter 5 for paper three. A brief outline of the three papers can be stated as follows.
The first paper studies a univariate forecasting model using the hybrid of asymmetric generalised autoregressive conditional heteroskedasticity and intertemporal capital asset pricing, with the following innovations: (1) a mixture of two generalised Pareto distributions and a Gaussian distribution; and (2) generalised error distribution. The Griddy Gibbs sampling algorithm in the Bayesian Markov chain Monte Carlo with parallel computing is used for the model parameter estimation. The study demonstrates the proposed model and estimation method through both simulation and empirical experiments among the benchmarks. It proves that the proposed model statistically outperforms competing models in the return forecasting under the conditions of market turmoil during the COVID-19 period.
The second paper extends the first paper from the univariate forecasting model to a multivariate forecasting model using high dimensional data and up to 100 dimensions where the comovement model is a regular vine model. The paper initiates a magnitude 13 bivariate copula candidate for the pair structure well-known in the literature of quantitative risk management. While the estimation techniques for the current paper explore another Bayesian Markov chain Monte Carlo, which is random-walk Metropolis-Hasting sampling, and, in Bayesian machine learning, variational Bayes with (and without) latent variables and data augmentation. Both simulation results and empirical results show satisfactory outcomes, since the proposed model and its estimation can outperform the traditional model.
The third paper extends multivariate regular vine forecasting model to the problem of dynamic optimal asset allocation in variate optimisation models. The study introduces evolutionary optimisation algorithms, including a genetic algorithm and a clonal selection algorithm, to optimisation problems. There are two main scenarios in optimisation problems which correspond to three model performance indicators: (1) the reward-risk indicator, (2) the diversity indicator, and (3) the convergence indicator. In addition, stock selection analysis is also applied to the optimisation problem. The empirical studies show that the proposed vine-copula-based forecasting model performs well in optimisation problems in terms of performance measures. Furthermore, based on the scenario experiment, the paper mathematically reveals that the financial market dependence structure has been disrupted as if a new normal has been established since the impact of the COVID-19 pandemic
Pricing Leveraged ETFS Options Under Heston Dynamics
No full textThe aim of this thesis is to derive a pricing formula for options on leverage exchange-traded funds (LETFs) with the assumption that the underlying index follows the Heston model dynamics. In order to price options for LETFs, we first establish a relationship between the price of an LETF and the value of its underlying index. This relationship is dependent on the leverage ratio of the LETF and the volatility of the underlying index. Through empirical analysis, we are able to justify the accuracy of this link between an LETF and its underlying index. Furthermore, this link provides useful information on the behaviour of LETFs which is studied in depth. We also use an optimization technique to provide empirically estimated leverage ratios for various LETFs of VIX and several equities to understand their behaviour under different market conditions. The option pricing formula is derived by defining the joint moment-generating function of the underlying index and its volatility and linking this function to the characteristic function of an LETF. The Carr-Madan Fourier transform method is utilized to obtain a closed-form solution of option prices in the form of an integral. We then numerically calculate the call option prices for specific parameters. We perform extensive analysis on our model. The call prices calculated from our option pricing formula are compared with those obtained by Monte-Carlo simulations and the results are consistent, justifying the use of our model. Finally, we perform sensitivity analysis to analyze the effect of various parametric changes on our model
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