Portfolio Optimization Under Multiscale Stochastic Volatility

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Portfolio Optimization Under Multiscale Stochastic Volatility

Author : Keqin Gong
Publisher :
ISBN 13 : 9781303151552
Total Pages : 84 pages
Book Rating : 4.1/5 (515 download)

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Book Synopsis Portfolio Optimization Under Multiscale Stochastic Volatility by : Keqin Gong

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.

Portfolio Optimization & Stochastic Volatility Asymptotics

Author : Jean-Pierre Fouque
Publisher :
ISBN 13 :
Total Pages : 37 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Portfolio Optimization & Stochastic Volatility Asymptotics by : Jean-Pierre Fouque

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.

Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives

Author : Jean-Pierre Fouque
Publisher : Cambridge University Press
ISBN 13 : 9780521843584
Total Pages : 456 pages
Book Rating : 4.8/5 (435 download)

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Book Synopsis Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives by : Jean-Pierre Fouque

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.

Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives

Author : Jean-Pierre Fouque
Publisher : Cambridge University Press
ISBN 13 : 113950245X
Total Pages : 456 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives by : Jean-Pierre Fouque

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.

Optimal Trading with Predictable Return and Stochastic Volatility

Author : Patrick Chan
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Optimal Trading with Predictable Return and Stochastic Volatility by : Patrick Chan

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.

Second Order Multiscale Stochastic Volatility Asymptotics

Author : Jean-Pierre Fouque
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Second Order Multiscale Stochastic Volatility Asymptotics by : Jean-Pierre Fouque

Download or read book Second Order Multiscale Stochastic Volatility Asymptotics written by Jean-Pierre Fouque and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and S{ o}lna (2011, CUP) analyzes models in which the volatility of the underlying is driven by two diffusions -- one fast mean-reverting and one slow-varying, and provides a first order approximation for European option prices and for the implied volatility surface, which is calibrated to market data. Here, we present the full second order asymptotics, which are considerably more complicated due to a terminal layer near the option expiration time. We find that, to second order, the implied volatility approximation depends quadratically on log-moneyness, capturing the convexity of the implied volatility curve seen in data. We introduce a new probabilistic approach to the terminal layer analysis needed for the derivation of the second order singular perturbation term, and calibrate to S&P 500 options data.

Portfolio Optimization Under Local-Stochastic Volatility

Author : Matthew Lorig
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Portfolio Optimization Under Local-Stochastic Volatility by : Matthew Lorig

Download or read book Portfolio Optimization Under Local-Stochastic Volatility written by Matthew Lorig and published by . This book was released on 2015 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the 'implied Sharpe ratio' and derive a series approximation for this quantity. The zeroth-order approximation of the value function and optimal investment strategy correspond to those obtained by Merton (1969) when the risky asset follows a geometric Brownian motion. The first-order correction of the value function can, for general utility functions, be expressed as a differential operator acting on the zeroth-order term. For power utility functions, higher order terms can also be computed as a differential operator acting on the zeroth-order term. We give a rigorous accuracy bound for the higher order approximations in this case in pure stochastic volatility models. A number of examples are provided in order to demonstrate numerically the accuracy of our approximations.

Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

Author : Katherine Yvonne Varga
Publisher :
ISBN 13 :
Total Pages : 112 pages
Book Rating : 4.:/5 (93 download)

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Book Synopsis Portfolio Optimization with Stochastic Dividends and Stochastic Volatility by : Katherine Yvonne Varga

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:

The Effect of Stochastic Volatility on Portfolio Optimization with Transaction Costs

Author : Scott M. Weiner
Publisher :
ISBN 13 :
Total Pages : 454 pages
Book Rating : 4.:/5 (454 download)

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Book Synopsis The Effect of Stochastic Volatility on Portfolio Optimization with Transaction Costs by : Scott M. Weiner

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:

Portfolio Optimization and Statistics in Stochastic Volatility Markets

Author : Carl Lindberg
Publisher :
ISBN 13 : 9789172916838
Total Pages : 11 pages
Book Rating : 4.9/5 (168 download)

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Book Synopsis Portfolio Optimization and Statistics in Stochastic Volatility Markets by : Carl Lindberg

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:

Derivatives in Financial Markets with Stochastic Volatility

Author : Jean-Pierre Fouque
Publisher : Cambridge University Press
ISBN 13 : 9780521791632
Total Pages : 222 pages
Book Rating : 4.7/5 (916 download)

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Book Synopsis Derivatives in Financial Markets with Stochastic Volatility by : Jean-Pierre Fouque

Download or read book Derivatives in Financial Markets with Stochastic Volatility written by Jean-Pierre Fouque and published by Cambridge University Press. This book was released on 2000-07-03 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.

Optimal Investment Under Multi-Factor Stochastic Volatility

Author : Marcos Escobar
Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Optimal Investment Under Multi-Factor Stochastic Volatility by : Marcos Escobar

Download or read book Optimal Investment Under Multi-Factor Stochastic Volatility written by Marcos Escobar and published by . This book was released on 2015 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a model for multivariate intertemporal portfolio choice in complete and incomplete markets with multi-factor stochastic covariance matrix of asset returns. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices: S&P500 and DAX. It is also shown that the model satisfies several stylized facts well known in the literature. We analyse the welfare losses due to suboptimal investment strategies and we find that the investors who invest myopically/ignore derivative assets/model volatility by one factor and ignore stochastic covariance between asset returns can incur significant welfare losses.

Merton's Portfolio Optimization Problem in a Black & Scholes Market with Non-Gaussian Stochastic Volatility of Ornstrein-Uhlenbeck Type

Download Merton's Portfolio Optimization Problem in a Black & Scholes Market with Non-Gaussian Stochastic Volatility of Ornstrein-Uhlenbeck Type PDF Online Free

Author : Fred E. Benth
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (594 download)

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Book Synopsis Merton's Portfolio Optimization Problem in a Black & Scholes Market with Non-Gaussian Stochastic Volatility of Ornstrein-Uhlenbeck Type by : Fred E. Benth

Download or read book Merton's Portfolio Optimization Problem in a Black & Scholes Market with Non-Gaussian Stochastic Volatility of Ornstrein-Uhlenbeck Type written by Fred E. Benth and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities

Author : Jean-Pierre Fouque
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities by : Jean-Pierre Fouque

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.

Stochastic Correlation and Portfolio Optimization by Multivariate Garch

Author : Cuicui Luo
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (133 download)

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Book Synopsis Stochastic Correlation and Portfolio Optimization by Multivariate Garch by : Cuicui Luo

Download or read book Stochastic Correlation and Portfolio Optimization by Multivariate Garch written by Cuicui Luo and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling time varying volatility and correlation in financial time series is an important element in derivative pricing, risk management and portfolio management. The main goal of this thesis is to investigate the performance of multivariate GARCH model in stochastic correlation forecast and apply theses techniques to develop a new model to enhance the dynamic portfolio performance in several context, including hedge fund portfolio construction.\\ First, we examine the performance of various univariate GARCH models and regime-switching stochastic volatility models in crude oil market. Then these univariate models discussed are extended to multivariate settings and the empirical evaluation provides evidence on the use of the orthogonal GARCH in correlation forecasting and risk management performance when an equally weighted portfolio is considered. \\ The recent financial turbulence exposed and raised serious concerns about the optimal portfolio selection problem in hedge funds. The dynamic portfolio construction performance of a broad set of multivariate stochastic volatility models is examined in a fund of hedge fund context. It provides further evidence on the use of the orthogonal GARCH in dynamic portfolio constructions and risk management. \\ Further in this work, a new portfolio optimization model is proposed in order to improve the dynamic portfolio performance. We enhance the safety-first model with standard deviation constraint and derive an analytic formula by filtering the returns with GH skewed t distribution and OGARCH. It is found that the proposed model outperforms the classical Mean-Variance model and Mean-CVAR model during financial crisis period for a fund of hedge fund.

Modeling, Stochastic Control, Optimization, and Applications

Author : George Yin
Publisher : Springer
ISBN 13 : 3030254984
Total Pages : 599 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Modeling, Stochastic Control, Optimization, and Applications by : George Yin

Download or read book Modeling, Stochastic Control, Optimization, and Applications written by George Yin and published by Springer. This book was released on 2019-07-16 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

International Portfolio Choice Under Multi-Factor Stochastic Volatility

Author : Marcos Escobar
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis International Portfolio Choice Under Multi-Factor Stochastic Volatility by : Marcos Escobar

Download or read book International Portfolio Choice Under Multi-Factor Stochastic Volatility written by Marcos Escobar and published by . This book was released on 2016 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a model of international portfolio choice in complete and incomplete markets with stochastic covariance between financial asset returns and exchange rates. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices, S &P500 and DAX using the USD-EUR exchange rate. We analyse the welfare losses due to various suboptimal investment strategies, in particular we find that investors who invest myopically in complete markets or ignore derivative assets can incur substantial welfare losses. Furthermore, we find strong evidence that the welfare benefits from international diversification are significant. It is also shown that the model satisfies several stylized facts well known in the literature for the equity market.