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Author: Patrick Chan
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
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: Patrick Chan
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
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: Pierre Collin-Dufresne
Publisher:
ISBN:
Category :
Languages : en
Pages : 57
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Book Description
We propose a simple approach to dynamic multi-period portfolio choice with transaction costs that is tractable in settings with a large number of securities, realistic return dynamics with multiple risk factors, many predictor variables, and stochastic volatility. We obtain a closed-form solution for an optimal trading rule when the problem is restricted to a broad class of strategies we define as 'linearity generating strategies' (LGS). When restricted to this class, the non-linear dynamic optimization problem reduces to a deterministic linear-quadratic optimization problem in the parameters of the trading strategies. We show that the LGS approach dominates several alternatives in realistic settings, and in particular when the covariance structure and transaction costs are stochastic.
Author: Patrick Cheridito
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
We study the problem of optimally liquidating a financial position in a discrete-time model with stochastic volatility and liquidity. We consider the three cases where the objective is to minimize the expectation, an expected exponential and a mean-variance criterion of the implementation cost. In the first case, the optimal solution can be fully characterized by a forward-backward system of stochastic equations depending on conditional expectations of future liquidity. In the other two cases we derive Bellman equations from which the optimal solutions can be obtained numerically by discretizing the control space. In all three cases we compute optimal strategies for different simulated realizations of prices, volatility and liquidity and compare the outcomes to the ones produced by the deterministic strategies of Bertsimas and Lo and Almgren and Chriss.
Author: Florian Ielpo
Publisher: Elsevier
ISBN: 0081011482
Category : Business & Economics
Languages : en
Pages : 432
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Book Description
Engineering Investment Process: Making Value Creation Repeatable explores the quantitative steps of a financial investment process. The authors study how these steps are articulated in order to make any value creation, whatever the asset class, consistent and robust. The discussion includes factors, portfolio allocation, statistical and economic backtesting, but also the influence of negative rates, dynamical trading, state-space models, stylized facts, liquidity issues, or data biases. Besides the quantitative concepts detailed here, the reader will find useful references to other works to develop an in-depth understanding of an investment process. Blends academic research with practical experience from quants, fund managers, and economists Puts financial mathematics and econometrics in their rightful place Presents useful information that will increase the reader's understanding of markets Clearly provides both the global framework, the investment process, and the useful econometric and financial tools that help in its construction Includes efficient tools taken from up-to-date econometric and financial techniques
Author: Jean-Pierre Fouque
Publisher: Cambridge University Press
ISBN: 113950245X
Category : Mathematics
Languages : en
Pages : 456
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Book Description
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: Robert A. Meyers
Publisher: Springer Science & Business Media
ISBN: 1441977007
Category : Business & Economics
Languages : en
Pages : 919
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Book Description
Finance, Econometrics and System Dynamics presents an overview of the concepts and tools for analyzing complex systems in a wide range of fields. The text integrates complexity with deterministic equations and concepts from real world examples, and appeals to a broad audience.
Author: Albert N. Shiryaev
Publisher: Springer Science & Business Media
ISBN: 0387283595
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Since the pioneering work of Black, Scholes, and Merton in the field of financial mathematics, research has led to the rapid development of a substantial body of knowledge, with plenty of applications to the common functioning of the world’s financial institutions. Mathematics, as the language of science, has always played a role in the development of knowledge and technology. Presently, the high-tech character of modern business has increased the need for advanced methods, which rely to a large extent on mathematical techniques. It has become essential for the financial analyst to possess a high degree of proficiency in these mathematical techniques.
Author: Alireza Javaheri
Publisher: John Wiley & Sons
ISBN: 1118161025
Category : Business & Economics
Languages : en
Pages : 222
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Book Description
Today?s traders want to know when volatility is a sign that the sky is falling (and they should stay out of the market), and when it is a sign of a possible trading opportunity. Inside Volatility Arbitrage can help them do this. Author and financial expert Alireza Javaheri uses the classic approach to evaluating volatility -- time series and financial econometrics -- in a way that he believes is superior to methods presently used by market participants. He also suggests that there may be "skewness" trading opportunities that can be used to trade the markets more profitably. Filled with in-depth insight and expert advice, Inside Volatility Arbitrage will help traders discover when "skewness" may present valuable trading opportunities as well as why it can be so profitable.
Author: Luc Bauwens
Publisher: John Wiley & Sons
ISBN: 1118272056
Category : Business & Economics
Languages : en
Pages : 566
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Book Description
A complete guide to the theory and practice of volatility models in financial engineering Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency. Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility: Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.
Author: Tim Leung (Professor of industrial engineering)
Publisher: World Scientific
ISBN: 9814725927
Category : Business & Economics
Languages : en
Pages : 221
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Book Description
"Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications provides a systematic study to the practical problem of optimal trading in the presence of mean-reverting price dynamics. It is self-contained and organized in its presentation, and provides rigorous mathematical analysis as well as computational methods for trading ETFs, options, futures on commodities or volatility indices, and credit risk derivatives. This book offers a unique financial engineering approach that combines novel analytical methodologies and applications to a wide array of real-world examples. It extracts the mathematical problems from various trading approaches and scenarios, but also addresses the practical aspects of trading problems, such as model estimation, risk premium, risk constraints, and transaction costs. The explanations in the book are detailed enough to capture the interest of the curious student or researcher, and complete enough to give the necessary background material for further exploration into the subject and related literature. This book will be a useful tool for anyone interested in financial engineering, particularly algorithmic trading and commodity trading, and would like to understand the mathematically optimal strategies in different market environments."--
