Stochastic Volatility Long Term Option And Discrete Time Problems In Fx

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Stochastic Volatility Long Term Option And Discrete Time Problems In Fx

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Author : Francois-Stephane Robert Mantion
language : en
Publisher:
Release Date : 1998

Stochastic Volatility Long Term Option And Discrete Time Problems In Fx written by Francois-Stephane Robert Mantion and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Stochastic Volatility Long Term Options And Discrete Time Problems In Fx

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Author : Francois-Stephane Robert Andre Mantion
language : en
Publisher:
Release Date : 1998

Stochastic Volatility Long Term Options And Discrete Time Problems In Fx written by Francois-Stephane Robert Andre Mantion and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Stochastic Volatility Option Pricing In Discrete Time

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Author : Victor K. Ng
language : en
Publisher:
Release Date : 1991

Stochastic Volatility Option Pricing In Discrete Time written by Victor K. Ng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Options (Finance) categories.

Option Pricing With Long Memory Stochastic Volatility Models

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Author : Zhigang Tong
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2013

Option Pricing With Long Memory Stochastic Volatility Models written by Zhigang Tong and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.

It is now known that long memory stochastic volatility models can capture the well-documented evidence of volatility persistence. However, due to the complex structures of the long memory processes, the analytical formulas for option prices are not available yet. In this book, we propose two fractional continuous time stochastic volatility models which are built on the popular short memory stochastic volatility models. Using the tools from stochastic calculus, fractional calculus and Fourier transform, we derive the (approximate) analytical solutions for option prices. We also numerically study the effects of long memory on option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter. We also find that long memory models can accommodate the short term options and the decay of volatility skew better than the corresponding short memory models. These findings would appeal to the researchers and practitioners in the areas of quantitative finance.

Volatility Surface And Term Structure

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Author : Kin Keung Lai
language : en
Publisher: Routledge
Release Date : 2013-09-11

Volatility Surface And Term Structure written by Kin Keung Lai and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-11 with Business & Economics categories.

This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.

Long Range Stochastic Volatility With Two Scales In Option Pricing

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Author : Li Kong
language : en
Publisher:
Release Date : 2012

Long Range Stochastic Volatility With Two Scales In Option Pricing written by Li Kong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.

We exploit a general framework, a martingale approach method, to estimate the derivative price for different stochastic volatility models. This method is a very useful tool for handling non-markovian volatility models. With this method, we get the order of the approximation error by evaluating the orders of three error correction terms. We also summarize some challenges in using the martingale approach method to evaluate the derivative prices. We propose two stochastic volatility models. Our goal is to get the analytical solution for the derivative prices implied by the models. Another goal is to obtain an explicit model for the implied volatility and in particular how it depends on time to maturity. The first model we propose involves the increments of a standard Brownian Motion for a short time increment. The second model involves fractional Brownian Motion(fBm) and two scales. By using fBm in our model, we naturally incorporate a long-range dependence feature of the volatility process. In addition, the implied volatility corresponding to our second model capture a feature of the volatility as observed in the paper Maturity cycles in implied volatility by Fouque, which analyzed the S & P 500 option price data and observed that for long dated options the implied volatility is approximately affine in the reciprocal of time to maturity, while for short dated options the implied volatility is approximately affine in the reciprocal of square root of time to maturity. The leading term in the implied volatility also matches the case when we have time-dependent volatility in the Black-Scholes equation.

Complex Systems In Finance And Econometrics

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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-03

Complex Systems In Finance And Econometrics written by Robert A. Meyers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-03 with Business & Economics categories.

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.

Discrete Time Stochastic Volatility Model

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Author : Guojing Tang
language : en
Publisher:
Release Date : 2009

Discrete Time Stochastic Volatility Model written by Guojing Tang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.

Stochastic Volatility And Fx Option Pricing

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Author : Bernd Mahler
language : en
Publisher:
Release Date : 2010

Stochastic Volatility And Fx Option Pricing written by Bernd Mahler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.

This paper analyzes if the implied volatility surface of foreign exchange options should be modelled by using classical stochastic volatility option pricing models or if more complex models like the Stochastic Skew models recently proposed by Carr and Wu (2004) are required. For this purpose three stochastic volatility models including the Heston model (1993), a restricted Heston model, a Hull White (1987) Model as well as three Stochastic Skew models based on different Jump structures, are calibrated and applied to the pricing of EURUSD and USDJPY options issued on the German foreign exchange options retail market. The comparison of market prices and model prices indicate that both for EURUSUD and USDJPY Stochastic Skew models based on time-changed Lévy processes mostly outperform traditional stochastic volatility models like Heston in capturing highly skewed implied volatility surfaces.

On Stochastic Dominance Optionbounds In Discrete And Continuous Space And Time With Stochastic And Deterministic Volatility And Pricing With Constant Relative Risk Aversion

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Author : Eli Rose
language : en
Publisher:
Release Date : 2020

On Stochastic Dominance Optionbounds In Discrete And Continuous Space And Time With Stochastic And Deterministic Volatility And Pricing With Constant Relative Risk Aversion written by Eli Rose and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Business mathematics categories.

This thesis makes original contributions to the field of asset pricing, which is a field dedicated to describing the prices of financial instruments and their characteristics. The prices of these financial instruments are determined by the behavior of investors who buy and sell them, and so asset pricing is ultimately done by modeling the behavior of investors. One method for achieving this is through the framework of stochastic dominance. This thesis specifically deals with a specific class of financial instruments called European options and reviews the literature on stochastic dominance option pricing and discusses new methods for finding stochastic dominance bounds on options in both discrete and continuous time under both deterministic and stochastic volatility. The results presented here extends the works of Ritchken and Kuo (1988) and Perrakis and Ryan (1984). Furthermore, stochastic dominance bounds for Heston's (1993) stochastic volatility model are obtained under certain assumptions. Finally, this thesis extends the work of Carr and Madan (1999) and solves for the characteristic function of the call price given the physical characteristic function under the CRRA utility model.