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Alternative Models For Stochastic Volatility Corrections For Equity And Interest Rate Derivatives
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Book Synopsis Alternative Models for Stochastic Volatility Corrections for Equity and Interest Rate Derivatives by : Tianyu Liang
Download or read book Alternative Models for Stochastic Volatility Corrections for Equity and Interest Rate Derivatives written by Tianyu Liang and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: A lot of attention has been paid to the stochastic volatility model where the volatility is randomly fluctuating driven by an additional Brownian motion. In our work, we change the mean level in the mean-reverting process from a constant to a function of the underlying process. We apply our models to the pricing of both equity and interest rate derivatives. Throughout the thesis, a singular perturbation method is employed to derive closed-form formulas up to first order asymptotic solutions. We also implement multiplicative noise to arithmetic Ornstein-Uhlenbeck process to produce a wider variety of effects. Calibration and Monte Carlo simulation results show that the proposed model outperform Fouque's original stochastic volatility model during some particular window in history. A more efficient numerical scheme, the heterogeneous multi-scale method (HMM), is introduced to simulate the multi-scale differential equations discussed over the chapters.
Book Synopsis Stochastics Volatility Corrections for Interest Rate Models by :
Download or read book Stochastics Volatility Corrections for Interest Rate Models written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is mainly focused on how to price the interest rate derivatives by stochastic volatility models. We will use CIR model and introduce a new Ito process to the model with fast mean-reverting stochastic volatility to compute the corrections of interest rate derivatives. There is a significant difference of the shape of yield curves between the corrected model and original CIR model. It can also be used to price interest rate derivatives such as bond options.
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.
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.
Book Synopsis Extension of Stochastic Volatility Equity Models with Hull-White Interest Rate Process by : Lech A. Grzelak
Download or read book Extension of Stochastic Volatility Equity Models with Hull-White Interest Rate Process written by Lech A. Grzelak and published by . This book was released on 2014 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an extension of stochastic volatility equity models by a stochastic Hull-White interest rate component while assuming non-zero correlations between the underlying processes. We place these systems of stochastic differential equations in the class of affine jump diffusion - linear quadratic jump-diffusion processes (Duffie, Pan and Singleton, Cheng and Scaillet) so that the pricing of European products can be efficiently done within the Fourier cosine expansion pricing framework. We compare the new stochastic volatility Schobel-Zhu-Hull-White hybrid model with a Heston-Hull-White model, and also apply the models to price some hybrid structured derivatives that combine the equity and interest rate asset classes.
Book Synopsis Turbo-Charged Local Stochastic Volatility Models by : Ghislain Vong
Download or read book Turbo-Charged Local Stochastic Volatility Models written by Ghislain Vong and published by . This book was released on 2013 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article presents an alternative formulation of the standard Local Stochastic Volatility model (LSV) widely used for the pricing and risk-management of FX derivatives and to a lesser extent of equity derivatives. In the standard model, calibration is achieved by solving a non-linear two-factor Kolmogorov forward PDE, where a minimum number of vol points is required to achieve convergence of a finite difference implementation. In contrast, we propose to model the volatility process by a Markov chain defined over an arbitrary small number of states, so that calibration and pricing are achieved by solving a coupled system of one-factor PDEs. The practical benefits are twofolds: existing one-factor PDE solvers can be recycled to model stochastic volatility, while the reduction in number of discretisation points implies a speedup in execution time that enables real-time risk-management of large derivatives position.
Book Synopsis Pricing Long-Maturity Equity and FX Derivatives with Stochastic Interest Rates and Stochastic Volatility by : Alexander van Haastrecht
Download or read book Pricing Long-Maturity Equity and FX Derivatives with Stochastic Interest Rates and Stochastic Volatility written by Alexander van Haastrecht and published by . This book was released on 2011 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we extend the stochastic volatility model of Schouml;bel and Zhu (1999) by including stochastic interest rates. Furthermore we allow all driving model factors to be instantaneously correlated with each other, i.e. we allow for a correlation between the instantaneous interest rates, the volatilities and the underlying stock returns. By deriving the characteristic function of the log-asset price distribution, we are able to price European stock options in closed-form by Fourier inversion. Furthermore we present a Foreign Exchange generalization and show how the pricing of Forward-starting options like cliquets can be performed. Additionally we discuss the practical implementation of these new models.
Book Synopsis A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives by : Anders B. Trolle
Download or read book A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives written by Anders B. Trolle and published by . This book was released on 2006 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features correlations between innovations to forward rates and volatilities, quasi-analytical prices of zero-coupon bond options and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finite-dimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities. The model also performs well in forecasting interest rates and derivatives.
Book Synopsis Currency Derivative and International Term Structure Pricing in a Stochastic Interest Rate, Stochastic Volatility and Stochastic Jump Intensity World by : Shijun Liu
Download or read book Currency Derivative and International Term Structure Pricing in a Stochastic Interest Rate, Stochastic Volatility and Stochastic Jump Intensity World written by Shijun Liu and published by . This book was released on 2007 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We first derive closed form solutions for currency options, currency futures, future options and the term structures of interest rates in a diffusion-jump model of stochastic interest rate, stochastic volatility and time varying jump intensity in currency price. We demonstrate that the introduction of constant jump intensity in the nominal stochastic discount factor shifts the whole term structure of interest rates vertically but has no influence on its shape. However, when the jump intensity is endogenous (time varying) the shape of the term structure is influenced through the factor sensitivity of interest rates. We also document considerable improvement in currency option pricing precision over alternative models if the true model is diffusion-jump with endogenous intensity in a simulation experiment. We conclude that allowing for multidimensional interaction is of significant qualitative and quantitative importance for the pricing of currency options and for understanding the shape of the term structure.
Book Synopsis Stochastic Volatility Corrections for Interest Rate Models by : Jin Dai
Download or read book Stochastic Volatility Corrections for Interest Rate Models written by Jin Dai and published by . This book was released on 2002 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: stochastic volatility corrections, Vasicek, CIR.
Author :Antoine Petrus Cornelius van der Ploeg Publisher :Rozenberg Publishers ISBN 13 :9051705778 Total Pages :358 pages Book Rating :4.0/5 (517 download)
Book Synopsis Stochastic volatility and the pricing of financial derivatives by : Antoine Petrus Cornelius van der Ploeg
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:
Book Synopsis Complex Systems in Finance and Econometrics by : Robert A. Meyers
Download or read book Complex Systems in Finance and Econometrics written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 919 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives by : Anders B. Trolle
Download or read book A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives written by Anders B. Trolle and published by . This book was released on 2016 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features unspanned stochastic volatility factors, correlation between innovations to forward rates and their volatilities, quasi-analytical prices of zero-coupon bond options, and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finitedimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities.
Book Synopsis Derivative Pricing Under Multivariate Stochastic Volatility Models with Application to Equity Options by : Mihaela Serban
Download or read book Derivative Pricing Under Multivariate Stochastic Volatility Models with Application to Equity Options written by Mihaela Serban and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Calibration and Simulation of Local Volatility Model with Stochastic Interest Rate by : Mingyang Xu
Download or read book On Calibration and Simulation of Local Volatility Model with Stochastic Interest Rate written by Mingyang Xu and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Local volatility model is a relatively simple way to capture volatility skew/smile. In spite of its drawbacks, it remains popular among practitioners for derivative pricing and hedging. For long-dated options or interest rate/equity hybrid products, in order to take into account the effect of stochastic interest rate on equity price volatility stochastic interest rate is often modelled together with stochastic equity price. Similar to local volatility model with deterministic interest rate, a forward Dupire PDE can be derived using Arrow-Debreu price method, which can then be shown to be equivalent to adding an additional correction term on top of Dupire forward PDE with deterministic interest rate. Calibrating a local volatility model by the forward Dupire PDE approach with adaptively mixed grids ensures both calibration accuracy and efficiency. Based on Malliavin calculus an accurate analytic approximation is also derived for the correction term incorporating impacts from both interest rate volatility and correlation, which integrates along a more likely straight line path for better accuracy. Eventually, the hybrid local volatility model can be calibrated in a two-step process, namely, calibrate local volatility model with deterministic interest rate and add adjustment for stochastic interest rate. Due to the lack of analytic solution and path-dependency nature of some products, Monte Carlo is a simple but flexible pricing method. In order to improve its convergence, we develop a scheme to combine merits of different simulation schemes and show its effectiveness.
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.
Book Synopsis Implied Volatility Functions by : Bernard Dumas
Download or read book Implied Volatility Functions written by Bernard Dumas and published by . This book was released on 1996 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black-Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset's return is a deterministic function of the asset price and time and develop the deterministic volatility function (DVF) option valuation model, which has the potential of fitting the observed cross-section of option prices exactly. Using a sample of S & P 500 index options during the period June 1988 through December 1993, we evaluate the economic significance of the implied deterministic volatility function by examining the predictive and hedging performance of the DV option valuation model. We find that its performance is worse than that of an ad hoc Black-Scholes model with variable implied volatilities.
