Analytical Approximations Of Option Prices In Stochastic Volatility Models
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Analytical Approximations Of Option Prices In Stochastic Volatility Models
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Author :
language : en
Publisher:
Release Date : 2007
Analytical Approximations Of Option Prices In Stochastic Volatility Models written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Stochastic Volatility Models Option Price Approximation Asymptotics And Maximum Likelihood Estimation
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Author : Jian Yang
language : en
Publisher:
Release Date : 2006
Stochastic Volatility Models Option Price Approximation Asymptotics And Maximum Likelihood Estimation written by Jian Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
An Analytical Approximation For European Option Prices Under Stochastic Interest Rate Economy
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Author : Hideharu Funahashi
language : en
Publisher:
Release Date : 2015
An Analytical Approximation For European Option Prices Under Stochastic Interest Rate Economy written by Hideharu Funahashi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
This paper extends the Wiener-Ito chaos expansion approach proposed by Funahashi and Kijima (2013) to an equity-interest-rate hybrid model for the pricing of European contingent claims with special emphasis on calibration to the option markets. Our model can capture the volatility skew and smile of option markets, as well as the stochastic nature of interest rates. Further, the proposed method is applicable to widely used option pricing models such as local volatility models, stochastic volatility models, and their combinations with the stochastic nature of interest rates; hence, it is suitable for practical purposes. Through numerical examples, we show that our approximation is quite accurate even for long-maturity and/or high-volatility cases.
Option Prices In Stochastic Volatility Models
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Author : Giulia Terenzi
language : en
Publisher:
Release Date : 2018
Option Prices In Stochastic Volatility Models written by Giulia Terenzi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
We study option pricing problems in stochastic volatility models. In the first part of this thesis we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic obstacle problem. Our approach is based on variational inequalities in suitable weighted Sobolev spaces and extends recent results of Daskalopoulos and Feehan (2011, 2016) and Feehan and Pop (2015). We also investigate the properties of the American value function. In particular, we prove that, under suitable assumptions on the payoff, the value function is nondecreasing with respect to the volatility variable. Then, we focus on an American put option and we extend some results which are well known in the Black and Scholes world. In particular, we prove the strict convexity of the value function in the continuation region, some properties of the free boundary function, the Early Exercise Price formula and a weak form of the smooth fit principle. This is done mostly by using probabilistic techniques.In the second part we deal with the numerical computation of European and American option prices in jump-diffusion stochastic volatility models. We first focus on the Bates-Hull-White model, i.e. the Bates model with a stochastic interest rate. We consider a backward hybrid algorithm which uses a Markov chain approximation (in particular, a “multiple jumps” tree) in the direction of the volatility and the interest rate and a (deterministic) finite-difference approach in order to handle the underlying asset price process. Moreover, we provide a simulation scheme to be used for Monte Carlo evaluations. Numerical results show the reliability and the efficiency of the proposed methods.Finally, we analyze the rate of convergence of the hybrid algorithm applied to general jump-diffusion models. We study first order weak convergence of Markov chains to diffusions under quite general assumptions. Then, we prove the convergence of the algorithm, by studying the stability and the consistency of the hybrid scheme, in a sense that allows us to exploit the probabilistic features of the Markov chain approximation.
A Mean Reverting Stochastic Volatility Option Pricing Model With An Analytic Solution
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Author : Henrik Andersson
language : en
Publisher:
Release Date : 2002
A Mean Reverting Stochastic Volatility Option Pricing Model With An Analytic Solution written by Henrik Andersson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
In this paper we derive a closed form approximation to a stochastic volatility option-pricing model and propose a variant of EGARCH for parameter estimation. The model thereby provides a consistent approach to the problem of option pricing and parameter estimation. Using Swedish stocks, the model provides a good fit to the heteroscedasticity prevalent in the time-series. The stochastic volatility model also prices options on the underlying stock more accurately than the traditional Black-Scholes formula. This result holds for both historic and implied volatility. A large part of the volatility smile that is observed for options of different maturity and exercise prices is thereby explained.
Modelling And Simulation Of Stochastic Volatility In Finance
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Author : Christian Kahl
language : en
Publisher: Universal-Publishers
Release Date : 2008
Modelling And Simulation Of Stochastic Volatility In Finance written by Christian Kahl and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Business & Economics categories.
The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black-Scholes model appropriately. Within this book the concept of stochastic volatility is analysed and discussed with special regard to the numerical problems occurring either in calibrating the model to the market implied volatility surface or in the numerical simulation of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives. We introduce a new stochastic volatility model, the so-called Hyp-Hyp model, and use Watanabe's calculus to find an analytical approximation to the model implied volatility. Further, the class of affine diffusion models, such as Heston, is analysed in view of using the characteristic function and Fourier inversion techniques to value European derivatives.
Closed Form Approximation Of Timer Option Prices Under General Stochastic Volatility Models
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Author : Minqiang Li
language : en
Publisher:
Release Date : 2013
Closed Form Approximation Of Timer Option Prices Under General Stochastic Volatility Models written by Minqiang Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
We develop an asymptotic expansion technique for pricing timer options under general stochastic volatility models around small volatility of variance. Closed-form approximation formulas have been obtained for the Heston model and the 3/2-model. The approximation has an easy-to-understand Black-Scholes-like form and many other attractive properties. Numerical analysis shows that the approximation formulas are very fast and accurate.
Analytical Green S Function Approximation And Option Pricing
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Author : Wen Cheng
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2011-10-18
Analytical Green S Function Approximation And Option Pricing written by Wen Cheng 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 2011-10-18 with categories.
Closed-form solutions to Kolmogorov type equations are very important in many application areas, such as derivative pricing, quantum mechanics, statistical physics, etc. However, they are only available for some very special equations. This book considers general second order parabolic equations with coefficients that are dependent on both time and space. It extends the recently developed Dyson-Taylor commutator method for autonomous equations to non-autonomous equations. Closed-form approximations of the Green's functions that are accurate to any prescribed order are obtained. Consequently, the solutions to second order parabolic equations can be obtained by integrating the approximated Green's functions against initial data. For applications, this book considers Local Volatility models and Stochastic Volatility models that appear in option pricing theory, gives explicit formulas for European option prices, and carries out numerical tests for such formulas.
Analytical Comparisons Of Option Prices In Stochastic Volatility Models
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Author : Vicky Henderson
language : en
Publisher:
Release Date : 2002
Analytical Comparisons Of Option Prices In Stochastic Volatility Models written by Vicky Henderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
An Analytical Approximation For Pricing Vwap Options
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Author : Hideharu Funahashi
language : en
Publisher:
Release Date : 2019
An Analytical Approximation For Pricing Vwap Options written by Hideharu Funahashi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
This paper proposes a unified approximation method for various options whose payoffs depend on the volume weighted average price (VWAP). Despite their popularity in practice, quite few pricing models have been developed in the literature. Also, in previous works, the underlying asset process has been restricted to a geometric Brownian motion. In contrast, our method is applicable to the general class of continuous Markov processes such as local volatility models, stochastic volatility models, and their combinations. Moreover, our method can be used for any type of VWAP options with fixed-strike, floating-strike, continuously sampled, discretely sampled, forward-start, and in-progress transactions.