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Author : Roman Horsky
Publisher :
ISBN 13 : 9783843906159
Total Pages : 223 pages
Book Rating : 4.9/5 (61 download)
Download or read book Barrier Option Pricing and CPPI-Optimization written by Roman Horsky and published by . This book was released on 2012 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (938 download)
Download or read book Barrier Option Pricing written by and published by . This book was released on 2009 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Don R. Rich
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
Download or read book The Mathematical Foundations of Barrier Option-Pricing Theory written by Don R. Rich and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Barrier options are one of the most popular first-generation exotic options, yet little theoretical research exists. This paper begins by presenting, in an intuitive and unified framework, the mathematical foundation necessary to value barrier options. Closed-form solutions are derived and comparative statics are presented for European barrier options with a fixed rebate and barrier level. From both a theoretical and hedging perspective, barrier options are shown to be more complex than standard options. Further, it is shown that under certain conditions barrier options are identical in value to standard options, that all valuation solutions are linearly homogeneous of degree one with respect to the underlying asset price, exercise price, barrier level, and rebate, and that barrier options have quite different hedging properties than standard options. Closed-form solutions are also derived for European barrier options with barriers that depend exponentially on time to expiration. Applications discussed in the paper include covered calls, portfolio insurance, options embedded in bonds, and when barrier option prices are more likely to correspond to observed market prices than Black-Scholes option prices.
Author : Zareer Dadachanji
Publisher : Springer
ISBN 13 : 1137462752
Total Pages : 274 pages
Book Rating : 4.1/5 (374 download)
Download or read book FX Barrier Options written by Zareer Dadachanji and published by Springer. This book was released on 2016-04-29 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Barrier options are a class of highly path-dependent exotic options which present particular challenges to practitioners in all areas of the financial industry. They are traded heavily as stand-alone contracts in the Foreign Exchange (FX) options market, their trading volume being second only to that of vanilla options. The FX options industry has correspondingly shown great innovation in this class of products and in the models that are used to value and risk-manage them. FX structured products commonly include barrier features, and in order to analyse the effects that these features have on the overall structured product, it is essential first to understand how individual barrier options work and behave. FX Barrier Options takes a quantitative approach to barrier options in FX environments. Its primary perspectives are those of quantitative analysts, both in the front office and in control functions. It presents and explains concepts in a highly intuitive manner throughout, to allow quantitatively minded traders, structurers, marketers, salespeople and software engineers to acquire a more rigorous analytical understanding of these products. The book derives, demonstrates and analyses a wide range of models, modelling techniques and numerical algorithms that can be used for constructing valuation models and risk-management methods. Discussions focus on the practical realities of the market and demonstrate the behaviour of models based on real and recent market data across a range of currency pairs. It furthermore offers a clear description of the history and evolution of the different types of barrier options, and elucidates a great deal of industry nomenclature and jargon.
Author : Jan H. Maruhn
Publisher : Walter de Gruyter
ISBN 13 : 3110208512
Total Pages : 210 pages
Book Rating : 4.1/5 (12 download)
Download or read book Robust Static Super-Replication of Barrier Options written by Jan H. Maruhn and published by Walter de Gruyter. This book was released on 2009-07-14 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Static hedge portfolios for barrier options are very sensitive with respect to changes of the volatility surface. To prevent potentially significant hedging losses this book develops a static super-replication strategy with market-typical robustness against volatility, skew and liquidity risk as well as model errors. Empirical results and various numerical examples confirm that the static superhedge successfully eliminates the risk of a changing volatility surface. Combined with associated sub-replication strategies this leads to robust price bounds for barrier options which are also relevant in the context of dynamic hedging. The mathematical techniques used to prove appropriate existence, duality and convergence results range from financial mathematics, stochastic and semi-infinite optimization, convex analysis and partial differential equations to semidefinite programming.
Author : Emmanuel Deogratias
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659362316
Total Pages : 124 pages
Book Rating : 4.3/5 (623 download)
Download or read book Methods for Pricing and Hedging Plain Vanilla Barrier Options written by Emmanuel Deogratias and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Black Scholes Model (1973) is used to price and hedge plain vanilla barrier options on a non dividend paying asset. Under this model, Monte Carlo Simulation, Stratified sampling, Simpson's rule, Trapezoidal rule and Antithetic variable techniques have been used to determine the value and hedging portfolio of a plain vanilla barrier option. Also stochastic dynamic programming has been developed so as to determine the price and hedging portfolio of the option. Finally the methods are compared to each other in terms of accuracy. It is found that stratified sampling technique is the best method after comparing with other methods.
Author : Martin Walter Günther
Publisher :
ISBN 13 :
Total Pages : 67 pages
Book Rating : 4.:/5 (17 download)
Download or read book Barrier option pricing through local time written by Martin Walter Günther and published by . This book was released on 2012 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudiger Kiesel
Publisher : World Scientific
ISBN 13 : 9814467332
Total Pages : 414 pages
Book Rating : 4.8/5 (144 download)
Download or read book Alternative Investments And Strategies written by Rudiger Kiesel and published by World Scientific. This book was released on 2010-06-18 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines academic research and practical expertise on alternative assets and trading strategies in a unique way. The asset classes that are discussed include: credit risk, cross-asset derivatives, energy, private equity, freight agreements, alternative real assets (ARA), and socially responsible investments (SRI). The coverage on trading and investment strategies are directed at portfolio insurance, especially constant proportion portfolio insurance (CPPI) and constant proportion debt obligation (CPDO) strategies, robust portfolio optimization, and hedging strategies for exotic options.
Author : Chi-Fai Lo
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (129 download)
Download or read book A Simple Approach for Pricing Barrier Options with Time-Dependent Parameters written by Chi-Fai Lo and published by . This book was released on 2007 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present a simple and easy-to-use method for computing accurate estimates (in closed form) of Black-Scholes barrier option prices with time-dependent parameters. This new approach is also able to provide tight upper and lower bounds (in closed form) for the exact barrier option prices.
Author : Ronald C. Heynen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
Download or read book Partial Barrier Options written by Ronald C. Heynen and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we study the pricing of barrier options where the period during which the underlying price is monitored for barrier hits is restricted to only part of the options' lifetime. We derive closed-form formulas for the prices of a number of partial barrier options, including partial asset- or-nothing and cash-or-nothing barrier options. Our results clearly show the importance of the length and the location of the monitoring period for the option price. It is also shown that for options where the monitoring period starts after the options' initial starting date, an alternative interpretation of the barrier condition may lead to a very substantial change in the option price.
Author : Sheldon Ross
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Efficient Monte Carlo Barrier Option Pricing When the Underlying Security Price Follows a Jump-Diffusion Process written by Sheldon Ross and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We present efficient simulation procedures for pricing barrier options when the underlying security price follows a geometric Brownian motion with jumps. Metwally and Atiya [2002] developed a simulation approach for pricing knock-out options in the same setting, but no variance reduction was introduced. We improve upon Metwally and Atiya's method by innovative applications of well-known variance reduction techniques. We also show how to use simulation to price knock-in options. Numerical examples show that our proposed Monte Carlo procedures lead to substantial variance reduction as well as a reduction in computing time.
Author : Junling Hu
Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.:/5 (891 download)
Download or read book Barrier Option Pricing Under SABR Model Using Monte Carlo Methods written by Junling Hu and published by . This book was released on 2013 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The project investigates the prices of barrier options from the constant underlying volatility in the Black-Scholes model to stochastic volatility model in SABR framework. The constant volatility assumption in derivative pricing is not able to capture the dynamics of volatility. In order to resolve the shortcomings of the Black-Scholes model, it becomes necessary to find a model that reproduces the smile effect of the volatility. To model the volatility more accurately, we look into the recently developed SABR model which is widely used by practitioners in the financial industry. Pricing a barrier option whose payoff to be path dependent intrigued us to find a proper numerical method to approximate its price. We discuss the basic sampling methods of Monte Carlo and several popular variance reduction techniques. Then, we apply Monte Carlo methods to simulate the price of the down-and-out put barrier options under the Black-Scholes model and the SABR model as well as compare the features of these two models.
Author : Fannu Hu
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Asymptotics of American Barrier Option Pricing written by Fannu Hu and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Justin Kirkby
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (13 download)
Download or read book Robust Barrier Option Pricing by Frame Projection Under Exponential Levy Dynamics written by Justin Kirkby and published by . This book was released on 2017 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an efficient method for robustly pricing discretely monitored barrier and occupation time derivatives under exponential Levy models. This includes ordinary barrier options, as well as (resetting) Parisian options, delayed barrier options (also known as cumulative Parisian or Parasian options), fader options, and step options (soft-barriers), all with single and double barriers, which have yet to be priced with more general Levy processes, including KoBoL (CGMY), Merton's jump diffusion and NIG. The method's efficiency is derived in part from the use of frame projected transition densities, which transform the problem into the Fourier domain, and accelerate the convergence of intermediate expectations. Moreover, these expectations are approximated by Toeplitz matrix-vector multiplications, resulting in a fast implementation. We devise an augmentation approach that contributes to the method's robustness, adding protection against mis-specifying a proper truncation support of the transition density. Theoretical convergence is verified by a series of numerical experiments which demonstrate the method's efficiency and accuracy.
Author : Sudip Chandra
Publisher :
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4.:/5 (13 download)
Download or read book Barrier Option Under Lévy Model written by Sudip Chandra and published by . This book was released on 2017 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Itô-Lévy calculus with the help of Mellin transform. The stock price is driven by a class of infinite activity Lévy processes leading to the market inherently incomplete, and dynamic hedging is no longer risk free. We first develop a PIDE for fixed type Barrier options, and apply the Mellin transform to derive a pricing expression. Our main contribution is to develop a PIDE with its closed form pricing expression for the contract. The procedure is easy to implement for all class of Lévy processes numerically. Finally, the algorithm for computing numerically is presented with results for a set of Lévy processes.
Author : Cho-Hoi Hui
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (129 download)
Download or read book Currency Barrier Option Pricing With Mean Reversion written by Cho-Hoi Hui and published by . This book was released on 2007 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a barrier-option pricing model in which the exchange rate follows a mean-reverting lognormal process. The corresponding closed-form solutions for the barrier options with time-dependent barriers are derived. The numerical results show that barrier option values and the corresponding hedge parameters under the proposed model are different from those based on the Black-Scholes model. For an up-and-out call, the mean-reverting process keeps the exchange rate in a small range around the mean level. When the mean level is below the barrier but above the strike price, the risk of the call to be knocked out is reduced and its option value is enhanced compared with the value under the Black-Scholes model. The parameters of the mean-reverting lognormal process therefore have a material impact on the valuation of currency barrier options and their hedge parameters.
Author : Chi-Fai Lo
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Valuing Time-Dependent CEV Barrier Options written by Chi-Fai Lo and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we have derived the analytical kernels of the pricing formulae of the CEV knockout options with time-dependent parameters for a parametric class of moving barriers. By a series of similarity transformations and changing variables, we are able to reduce the pricing equation to one which is reducible to the Bessel equation with constant parameters. These results enable us to develop a simple and efficient method for computing accurate estimates of the CEV single-barrier option prices as well as their upper and lower bounds when the model parameters are time-dependent. By means of the multi-stage approximation scheme, the upper and lower bounds for the exact barrier option prices can be efficiently improved in a systematic manner. It is also natural that this new approach can be easily applied to capture the valuation of other standard CEV options with specified moving knockout barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, more comparative pricing and precise risk management in equity options can be achieved by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.
