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Author: Zhibo Jia
Publisher:
ISBN:
Category :
Languages : en
Pages : 302
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Book Description
This thesis consists of three papers which cover the efficient Monte Carlo simulation in option pricing, the application of realized volatility in trading strategies and geometrical analysis of a four asset mean variance portfolio optimization problem. The first paper studies different efficient simulation methods to price options with different characters such as moneyness and maturity times. The incomplete market environments are also been considered. The second paper uses realized volatility based on high frequency data to improve the volatility trading strategy. The performance is compared with that using the implied volatility. The last paper re-examines the Markowitz's portfolio optimization problem using a general case. It also extends the problem to four assets, it describes the exact mean variance efficient fronter in the weight space and studies the frontier in the mean variance space. The thesis may serve to help our understanding of how to apply numerical and analytical methods to solve financial problems.
Author: Zhibo Jia
Publisher:
ISBN:
Category :
Languages : en
Pages : 302
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Book Description
This thesis consists of three papers which cover the efficient Monte Carlo simulation in option pricing, the application of realized volatility in trading strategies and geometrical analysis of a four asset mean variance portfolio optimization problem. The first paper studies different efficient simulation methods to price options with different characters such as moneyness and maturity times. The incomplete market environments are also been considered. The second paper uses realized volatility based on high frequency data to improve the volatility trading strategy. The performance is compared with that using the implied volatility. The last paper re-examines the Markowitz's portfolio optimization problem using a general case. It also extends the problem to four assets, it describes the exact mean variance efficient fronter in the weight space and studies the frontier in the mean variance space. The thesis may serve to help our understanding of how to apply numerical and analytical methods to solve financial problems.
Author: Erricos Kontoghiorghes
Publisher: Springer Science & Business Media
ISBN: 3540779582
Category : Business & Economics
Languages : en
Pages : 425
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Book Description
Computational models and methods are central to the analysis of economic and financial decisions. Simulation and optimisation are widely used as tools of analysis, modelling and testing. The focus of this book is the development of computational methods and analytical models in financial engineering that rely on computation. The book contains eighteen chapters written by leading researchers in the area on portfolio optimization and option pricing; estimation and classification; banking; risk and macroeconomic modelling. It explores and brings together current research tools and will be of interest to researchers, analysts and practitioners in policy and investment decisions in economics and finance.
Author: Zhen Liu
Publisher:
ISBN: 9781109968606
Category : Asset allocation
Languages : en
Pages : 54
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Book Description
Portfolio optimization problems with transaction costs have been widely studied by both financial economists and financial engineers through various approaches. In this paper, we propose the following approach. In analogy to American option pricing, we study the problem through the Finite Element Method (FEM) combined with an optimization method: We set up a buy-and-hold problem and then we find an optimal set of trades to move to an optimal portfolio whenever the current portfolio is far from the ideal. Local Discontinuous Galerkin (LDG) FEM is used to solve the partial differential equation (PDE) associated with the buy-and-hold problem. Coupled with the Runge-Kutta method for time discretization, this method is local with respect to spatial variable, can be used to achieve any order of accuracy and is explicit in the semi-discrete Ordinary Differential Equation (ODE) form. Also it is amendable to parallel computing. In this paper we give error bounds for the LDG method, with which we establish overall bounds for the portfolio optimization problem and prove the convergence of this method.
Author: Xiaolin Sun
Publisher:
ISBN:
Category : Portfolio management
Languages : en
Pages : 61
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Book Description
Estimating the volatilities and correlations of asset returns plays an important role in portfolio and risk management. As of late, interest in the estimation of the covariance matrix of large dimensional portfolios has increased. Estimating large dimensional covariance poses a challenge in that the cross-sectional dimension is often similar to or bigger than the number of observations available. Simple estimators are often poorly conditioned with some small eigenvalues, and so are unsuitable for many real world applications, including portfolio optimization and tracking error minimization. The first chapter introduces our two large dimensional covariance matrix estimators. We estimate the large dimensional realized covariance matrix by using the methods of asymptotic principal components analysis based factor modeling and singular value decomposition. In the second chapter, we show though simulation that our proposed estimators are closer to the true covariance matrix than the current popular shrinkage estimator. We also simulate conducting the out sample portfolio performance tests and find that the portfolios constructed based on our proposed estimators have lower risk than portfolios constructed using the shrinkage matrix. Using S&P 500 stocks from 1926 to 2011, we back test our proposed covariance matrix. In addition, the portfolios constructed based on our proposed estimators exhibit lower risk than portfolios constructed using the shrinkage matrix. The third chapter proposes a new volatility index--a cross-sectional volatility index of residuals using factor model. The cross-sectional volatility index moves closely with the VIX for the S&P 500 stock universe. It is a non-parametric, model-free volatility index, which could be estimated at any frequency for any region, sector, and style of world equity market and also does not depend on any option pricing. We provide some interpretation of the cross-sectional volatility index of residuals as a proxy for aggregate economic uncertainty, and show a high correlation between the VIX index and the corresponding cross-sectional volatility index of residuals based on the S&P 500 universe. Our results show that the portfolio hedged based on the cross-sectional volatility index of residuals has a much higher Sharpe ratio than the portfolio without hedge. Overall, these findings suggest that the cross-sectional volatility index of residuals is intimately related to other volatility measures where and when such measures are available, and that it can be used as a reliable proxy for volatility when such measures are not available.
Author: Alexandra Hansis
Publisher:
ISBN:
Category :
Languages : en
Pages : 211
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Author: Liyuan Chen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Mathieu Fournier
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Ti Zhou
Publisher:
ISBN:
Category : Portfolio management
Languages : en
Pages : 282
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Book Description
This dissertation is a contribution to the pricing and portfolio choice theory in incomplete markets. It consists of three self-contained but interlinked essays. In the first essay, we present a utility-based methodology for the valuation and the risk management of mortgage-backed securities subject to totally unpredictable prepayment risk. Incompleteness stems from its embedded pre-payment option which affects the security's cash flow pattern. The prepayment time is constructed via deterministic or stochastic hazard rate. The relevant indifference price consists of a linear term, corresponding to the remaining outstanding balance, and a nonlinear one that incorporates the investor's risk aversion and the interest payments generated by the mortgage contract. The indifference valuation approach is also extended to the case of homogeneous mortgage pools. In the second essay, using forward optimality criteria, we analyze a portfolio choice problem when the local risk tolerance is time-dependent and asymptotically linear in wealth. This class corresponds to a dynamic extension of the traditional (static) risk tolerances associated with the power, logarithmic and exponential utilities. We provide explicit solutions for the optimal investment strategies and wealth processes in an incomplete non-Markovian market with asset prices modelled as Ito processes. The methodology allows for measuring the investment performance in terms of a benchmark and alter-native market views. In the last essay, we extend the forward investment performance approach to study the optimal portfolio choice problem in an incomplete market driven by jump processes. The asset price is modelled by a one-dimensional Lévy-Itô process. We prove the existence of a forward performance process by restricting the local risk tolerance functions to be time-independent and linear in wealth. This yields only three types of performance measurement criteria, namely, exponential, power and logarithmic. The optimal portfolios are constructed via stochastic feedback controls under these criteria.
Author: Jung Hwang
Publisher:
ISBN:
Category : Portfolio management
Languages : en
Pages : 278
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Author: Illia Kovalenko
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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