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Author : Scott M. Weiner
Publisher :
ISBN 13 :
Total Pages : 454 pages
Book Rating : 4.:/5 (454 download)
Download or read book The Effect of Stochastic Volatility on Portfolio Optimization with Transaction Costs written by Scott M. Weiner and published by . This book was released on 2000 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Maxim Bichuch
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (13 download)
Download or read book Optimal Investment with Transaction Costs and Stochastic Volatility Part I written by Maxim Bichuch and published by . This book was released on 2015 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of asymptotic approximations when the cost is small. Under stochastic volatility, but with no transaction costs, the Merton problem under general utility functions can also be analyzed with asymptotic methods. Here, we look at the long-run growth rate problem when both complexities are present, using separation of time scales approximations. This leads to perturbation analysis of an eigenvalue problem. We find the first term in the asymptotic expansion in the time scale parameter, of the optimal long-term growth rate, and of the optimal strategy, for fixed small transaction costs.The Companion piece for this paper are available at the following URL: "http://ssrn.com/abstract=2659918" http://ssrn.com/abstract=2659918.
Author : Scott M. Weiner
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (129 download)
Download or read book Should Stochastic Volatility Matter to the Cost-Constrained Investor? written by Scott M. Weiner and published by . This book was released on 2003 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant strides have been made in the development of continuous-time portfolio optimization models since Merton (1969). Two independent advances have been the incorporation of transaction costs and time-varying volatility into the investor's optimization problem. Transaction costs generally inhibit investors from trading too often; they force the investor to choose between holding a suboptimal portfolio and reallocating the portfolio to the optimal allocation by incurring a fee. Several models, including Eastham and Hastings (1988) and Davis and Norman (1990), show that the investor can experience periods of passive investment (i.e., periods without transaction activity) as a result of transaction costs. Time-varying volatility, on the other hand, encourages trading activity, as it can result in an evolving optimal allocation of resources, as in Karatzas (1989). We examine the two-asset portfolio optimization problem when both elements are present. We show that the transaction cost framework in Korn (1998) can be extended to include a stochastic volatility process. We then specify a transaction cost model with stochastic volatility, based on Morton and Pliska (1995), and show that when the risk premium is linear in variance, the optimal strategy for the investor is independent of the level of volatility in the risky asset. We call this the Variance Invariance Principle.
Author : Patrick Chan
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (13 download)
Download or read book Optimal Trading with Predictable Return and Stochastic Volatility written by Patrick Chan and published by . This book was released on 2015 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a class of dynamic portfolio optimization problems that allow for models of return predictability, transaction costs, and stochastic volatility. Determining the dynamic optimal portfolio in this general setting is almost always intractable. We propose a multiscale asymptotic expansion when the volatility process is characterized by its time scales of fluctuation. The analysis of the nonlinear Hamilton- Jacobi-Bellman PDE is a singular perturbation problem when volatility is fast mean-reverting; and it is a regular perturbation when the volatility is slowly varying. These analyses can be combined for multifactor multiscale stochastic volatility model. We present formal derivations of asymptotic approximations and demonstrate how the proposed algorithms improve our Profit & Loss using Monte Carlo simulations.
Author : Katherine Yvonne Varga
Publisher :
ISBN 13 :
Total Pages : 112 pages
Book Rating : 4.:/5 (93 download)
Download or read book Portfolio Optimization with Stochastic Dividends and Stochastic Volatility written by Katherine Yvonne Varga and published by . This book was released on 2015 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 169 pages
Book Rating : 4.:/5 (911 download)
Download or read book Portfolio Optimization and Stochastic Control Under Transaction Costs written by and published by . This book was released on 2015 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jean-Pierre Fouque
Publisher : Cambridge University Press
ISBN 13 : 113950245X
Total Pages : 456 pages
Book Rating : 4.1/5 (395 download)
Download or read book Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives written by Jean-Pierre Fouque and published by Cambridge University Press. This book was released on 2011-09-29 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.
Author : Maxim Bichuch
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (13 download)
Download or read book Optimal Investment with Transaction Costs and Stochastic Volatility Part II written by Maxim Bichuch and published by . This book was released on 2018 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this companion paper to “Optimal Investment with Transaction Costs and Stochastic Volatility Part I: Infinite Horizon”, "http://ssrn.com/abstract=2374150" http://ssrn.com/abstract=2374150, we give an accuracy proof for the finite time optimal investment and consumption problem under fast mean-reverting stochastic volatility of a joint asymptotic expansion in a time scale parameter and the small transaction cost. The supplemental appendix accompanies this paper is, available at "http://ssrn.com/abstract=3234374" http://ssrn.com/abstract=3234374, in which we prove the verification theorem that the value function is a viscosity solution of the HJB equation.
Author : Ashri Rahadi
Publisher :
ISBN 13 :
Total Pages : 6 pages
Book Rating : 4.:/5 (13 download)
Download or read book Execute Trading Policies on Optimal Portfolio When Stochastic Volatility and Inflation Effect Were Considered written by Ashri Rahadi and published by . This book was released on 2016 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tempting to formulate the long-term investment strategy for investors who dynamically adjust her portfolio over her lifetime, we are interested to optimize the end-of-period terminal wealth using Bellman Principles. We designed the portfolio to be replete with risky asset and risk-less asset/fixed-income asset in the continuous framework. The stochastic volatility model is depicted in risky asset dynamic known as Constant Elasticity of Variance (CEV), because the empirical bias of Leverage effect in stock price evolution founded by Black Scholes can be directly examined. Meanwhile the bond pricing analysis was no longer classified as risk-free asset because it was analyzed under the stochastic Inflation and Interest rate of affine structures named Vasicek. Because we want to reflect their mean-reverting behavior as they're hovering around their long-term mean. Later, state space was constructed and portion of risky asset was elected to be control variables for supremum over value function. The concept of investment decision is intertemporal, as today decision affected tomorrow's, which finding its optimal rate would be trade-off for investor. For this, we framed the decision criteria with investor's utility function from class Decreasing Absolute Risk Aversion (DARA), the class that generally most investor mostly consistent with [Friend & Blumme 1975]. The problem description above can be represented as stochastic optimal control problem and it was solved with dynamic programming argument with modified verification theorem to tackle the issue of Stochastic Differential Equation well-posedness violation. Through stages of change variables, we were able to find the closed form trading solution from corresponding Hamilton Jacobi Bellman (HJB) equation. Compare to standard Merton model, our trading strategies strength are determining interest rate, inflation rate and degree of leverage for improvement and hence have inline economic logic reasoning for our solutions.
Author : Carl Lindberg
Publisher :
ISBN 13 : 9789172916838
Total Pages : 11 pages
Book Rating : 4.9/5 (168 download)
Download or read book Portfolio Optimization and Statistics in Stochastic Volatility Markets written by Carl Lindberg and published by . This book was released on 2005 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Keqin Gong
Publisher :
ISBN 13 : 9781303151552
Total Pages : 84 pages
Book Rating : 4.1/5 (515 download)
Download or read book Portfolio Optimization Under Multiscale Stochastic Volatility written by Keqin Gong and published by . This book was released on 2013 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, the classical Merton problem, a portfolio selection problem, is extended using multiscale volatility model which assumes that volatility of stock price depends on a fast scale process and a slow scale process. The Dynamic Programming Principle is used to establish the Hamilton-Jacobi-Bellman equation. An asymptotic method based on two small parameters from two scale factors, is applied in solving the equation to obtain an approximation of optimal trading strategy and value function, which is the expectation of utility of wealth in future. We also prove that when these two parameters are small, the error of our approximation of value function is small. Furthermore, we consider the counterparty risk in the portfolio selection problem, which means stock price has a jump at the default time and the stock is still tradable after default happens. In this scenario, an approximation of value function and optimal trading strategy is also derived and error of the approximation is estimated. Finally we use finite difference method to solve the problem and show how multiscale volatility model and counterparty default affect the results.
Author : Jean-Pierre Fouque
Publisher :
ISBN 13 :
Total Pages : 37 pages
Book Rating : 4.:/5 (13 download)
Download or read book Portfolio Optimization & Stochastic Volatility Asymptotics written by Jean-Pierre Fouque and published by . This book was released on 2015 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the Merton portfolio optimization problem in the presence of stochastic volatility using asymptotic approximations when the volatility process is characterized by its time scales of fluctuation. This approach is tractable because it treats the incomplete markets problem as a perturbation around the complete market constant volatility problem for the value function, which is well-understood. When volatility is fast mean-reverting, this is a singular perturbation problem for a nonlinear Hamilton-Jacobi-Bellman PDE, while when volatility is slowly varying, it is a regular perturbation. These analyses can be combined for multifactor multiscale stochastic volatility models. The asymptotics shares remarkable similarities with the linear option pricing problem, which follows from some new properties of the Merton risk-tolerance function. We give examples in the family of mixture of power utilities and also we use our asymptotic analysis to suggest a "practical" strategy which does not require tracking the fast-moving volatility. In this paper, we present formal derivations of asymptotic approximations, and we provide a convergence proof in the case of power utility and single factor stochastic volatility. We assess our approximation in a particular case where there is an explicit solution.
Author : E. Robert Fernholz
Publisher : Springer Science & Business Media
ISBN 13 : 1475736991
Total Pages : 190 pages
Book Rating : 4.4/5 (757 download)
Download or read book Stochastic Portfolio Theory written by E. Robert Fernholz and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios and for analyzing the effects induced on the behavior of these portfolios by changes in the distribution of capital in the market. Stochastic portfolio theory has both theoretical and practical applications: as a theoretical tool it can be used to construct examples of theoretical portfolios with specified characteristics and to determine the distributional component of portfolio return. This book is an introduction to stochastic portfolio theory for investment professionals and for students of mathematical finance. Each chapter includes a number of problems of varying levels of difficulty and a brief summary of the principal results of the chapter, without proofs.
Author : Maxim Bichuch
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (13 download)
Download or read book Supplemental Appendix to Optimal Investment with Transaction Costs and Stochastic Volatility Part II written by Maxim Bichuch and published by . This book was released on 2018 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: This supplemental appendix accompanies "Optimal Investment with Transaction Costs and Stochastic Volatility Part II: Finite Horizon" by the same authors, available at:"http://ssrn.com/abstract=2659918" http://ssrn.com/abstract=2659918. In this appendix we prove the verification theorem that the value function is a viscosity solution of the HJB equation.
Author : Jean-Pierre Fouque
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (13 download)
Download or read book Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities written by Jean-Pierre Fouque and published by . This book was released on 2019 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a continuous-time economy, we investigate the asset allocation problem among a risk-free asset and two risky assets with an ambiguous correlation between the two risky assets. The portfolio selection that is robust to the uncertain correlation is formulated as the utility maximization problem over the worst-case scenario with respect to the possible choice of correlation. Thus, it becomes a maximin problem. We solve the problem under the Black-Scholes model for risky assets with an ambiguous correlation using the theory of G-Brownian motions. We then extend the problem to stochastic volatility models for risky assets with an ambiguous correlation between risky asset returns. An asymptotic closed-form solution is derived for a general class of utility functions, including CRRA and CARA utilities, when stochastic volatilities are fast mean-reverting. We propose a practical trading strategy that combines information from the option implied volatility surfaces of risky assets through the ambiguous correlation.
Author : Ali N. Akansu
Publisher : John Wiley & Sons
ISBN 13 : 1118745647
Total Pages : 312 pages
Book Rating : 4.1/5 (187 download)
Download or read book Financial Signal Processing and Machine Learning written by Ali N. Akansu and published by John Wiley & Sons. This book was released on 2016-04-20 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modern financial industry has been required to deal with large and diverse portfolios in a variety of asset classes often with limited market data available. Financial Signal Processing and Machine Learning unifies a number of recent advances made in signal processing and machine learning for the design and management of investment portfolios and financial engineering. This book bridges the gap between these disciplines, offering the latest information on key topics including characterizing statistical dependence and correlation in high dimensions, constructing effective and robust risk measures, and their use in portfolio optimization and rebalancing. The book focuses on signal processing approaches to model return, momentum, and mean reversion, addressing theoretical and implementation aspects. It highlights the connections between portfolio theory, sparse learning and compressed sensing, sparse eigen-portfolios, robust optimization, non-Gaussian data-driven risk measures, graphical models, causal analysis through temporal-causal modeling, and large-scale copula-based approaches. Key features: Highlights signal processing and machine learning as key approaches to quantitative finance. Offers advanced mathematical tools for high-dimensional portfolio construction, monitoring, and post-trade analysis problems. Presents portfolio theory, sparse learning and compressed sensing, sparsity methods for investment portfolios. including eigen-portfolios, model return, momentum, mean reversion and non-Gaussian data-driven risk measures with real-world applications of these techniques. Includes contributions from leading researchers and practitioners in both the signal and information processing communities, and the quantitative finance community.
Author : Denis Matthias Schelling
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (119 download)
Download or read book Rough Volatility and Portfolio Optimisation Under Small Transaction Costs written by Denis Matthias Schelling and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
