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.
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.
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.
Download or read book Optimal Portfolios written by Ralf Korn and published by World Scientific. This book was released on 1997 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc. Stress is laid on rigorous mathematical presentation and clear economic interpretations while technicalities are kept to the minimum. The underlying mathematical concepts will be provided. No a priori knowledge of stochastic calculus, stochastic control or partial differential equations is necessary (however some knowledge in stochastics and calculus is needed).
Download or read book Optimal Investment with Two Factor Uncertainty written by Manuel J. Rocha Armada and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a real options model to value the option to invest in a new project, whose value is contingent on two multiplicative stochastic factors behaving accordingly to correlated geometric Brownian motions. A general sensitivity analysis is conducted highlighting the importance of the variance and correlation between the two variables. A higher correlation is shown to increase always the values of the trigger, the active project and the option. The impact of uncertainty is more complex and depends on the assumption about which variables adjust and the correlation between the variables and the market as a whole. Uncertainty can, for some cases, decrease the trigger and the option values, namely when the correlation with the market is negative and the growth rates are fixed, and when the two stochastic variables are highly negatively correlated.
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.
Download or read book Uncertain Volatility Models written by Robert Buff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the only books to describe uncertain volatility models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets. Uncertain volatility models place subjective constraints on the volatility of the stochastic process of the underlying asset and evaluate option portfolios under worst- and best-case scenarios. This book, which is bundled with software, is aimed at graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options. The reader is assumed to be familiar with arbitrage pricing theory.
Download or read book Optimal Investment Problem in Stochastic and Local Volatility Models written by Vladimir Piterbarg and published by . This book was released on 2018 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: We revisit the classical Merton's optimal allocation problem and show that significant corrections to the Merton ratio arise from hard to observe behaviour of the volatility process around zero. Having regularised this behaviour, we show that the adjustment to the myopic Merton ratio can be largely deduced from observed option prices, which paves the way to a practical approach to the more efficient asset allocation.
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.
Download or read book Robust Utility Maximization in a Stochastic Factor Model written by and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We give an explicit PDE characterization for the solution of a robust utility maximization problem in an incomplete market model, whose volatility, interest rate process, and long-term trend are driven by an external stochastic factor process. The robust utility functional is defined in terms of a HARA utility function with negative risk aversion and a dynamically consistent coherent risk measure, which allows for model uncertainty in the distributions of both the asset price dynamics and the factor process. Our method combines two recent advances in the theory of optimal investments: the general duality theory for robust utility maximization and the stochastic control approach to the dual problem of determining optimal martingale measures. -- optimal investment ; model uncertainty ; incomplete markets ; stochastic volatility ; coherent risk measures ; optimal control ; convex duality
Download or read book Optimal Investment in Incomplete Markets with Multiple Brownian Externalities written by Levon Avanesyan and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An investor?s optimal market portfolio is shaped by their investment performance criterion. The latter is largely determined by the investor's idiosyncratic objectives and preferences. This dissertation contributes to the study of optimal investment under the expected utility of terminal wealth (Merton), as well as forward performance criteria. Our set-up is that of a continuous incomplete stock market model, where the incompleteness stems from multiple Brownian externalities. The externalities manifest themselves through the stock return and volatility coefficients, either explicitly by driving observable stochastic factors or implicitly by increasing the market filtration.In a Markovian multifactor market model we introduce the eigenvalue equality (EVE) stock-factor correlation structure, and construct a large class of forward performance processes (FPPs) with power-utility initial data, as well as their corresponding optimal portfolios. This is done by solving the associated non-linear parabolic partial differential equations (PDEs) posed in the ``wrong'' time direction. We establish on domains an explicit form of the generalized Widder's theorem of Nadtochiy and Tehranchi (Math. Financ. 27:438-470, 2015, Theorem 3.12) and rely hereby on the Laplace inversion in time of the solutions to suitable linear parabolic PDEs posed in the "right'' time direction.Next, we consider the Merton problem with power utility in a market model with the stock coefficients adapted to a factor-generated filtration. This setup admits market models with non-semimartingale factors. For models with EVE structure we find the optimal portfolio weights up to the computation of a certain conditional expectation, and explain how to evaluate the latter in affine Volterra factor models. We extend these results to a general stock-factor correlation setting for, what we will call, Sharpe ratio separable (SRS) market models.In our most general market model, we construct a broad class of FPPs with initial conditions of power mixture type, [mathematical formula omitted]. We derive the properties of two-power mixture FPPs when the risk aversion coefficients are continuous stochastic processes in (0,1), and provide a full characterization when the coefficients are constants. Finally, we discuss the problem of managing an investment pool of two investors, whose respective preferences evolve as power FPPs.
Download or read book Optimal Investment written by L. C. G. Rogers and published by Springer Science & Business Media. This book was released on 2013-01-10 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readers of this book will learn how to solve a wide range of optimal investment problems arising in finance and economics. Starting from the fundamental Merton problem, many variants are presented and solved, often using numerical techniques that the book also covers. The final chapter assesses the relevance of many of the models in common use when applied to data.
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.
Download or read book Sustainability of the Theories Developed by Mathematical Finance and Mathematical Economics with Applications written by Wing-Keung Wong and published by MDPI. This book was released on 2020-12-15 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics studied in this Special Issue include a wide range of areas in finance, economics, tourism, management, marketing, and education. The topics in finance include stock market, volatility and excess returns, REIT, warrant and options, herding behavior and trading strategy, supply finance, and corporate finance. The topics in economics including economic growth, income poverty, and political economics.
Download or read book Stochastic Volatility for Real written by Jesper Andreasen and published by . This book was released on 2006 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: We combine classical ideas of separable volatility structures in the HJM framework with the latest techniques for calibration of stochastic volatility models and create a new class of efficient multi-factor term structure models with stochastic volatility. These models have the flexibility of as the Libor market models but the speed of the short rate models.
Download or read book Strategic Investment Decisions Under Fast Mean reversion Stochastic Volatility written by Max O. Souza and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We are concerned with investment decisions when the spanning asset that correlates with the investment value undergoes a stochastic volatility dynamics. The project value in this case corresponds to the value of an American call with dividends, which can be priced by solving a generalized Black-Scholes free boundary value problem. Following ideas of Fouque et al., under the hypothesis of fast mean reversion, we obtain the formal asymptotic expansion of the project value and compute the adjustment of the price due to the stochastic volatility. We show that the presence of the stochastic volatility can alter the optimal time investment curve in a significative way, which in turn implies that caution should be taken with the assumption of constant volatility prevalent in many real option models. Additionally, we also present analytical results for the perpetual case. We also indicate how to calibrate to market data the model in the asymptotic regime.
Download or read book Stochastic volatility and the pricing of financial derivatives written by Antoine Petrus Cornelius van der Ploeg and published by Rozenberg Publishers. This book was released on 2006 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
