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Jump Diffusion Processes Discrete Time Option Replication And Pricing European Call Options In The Presence Of Transaction Costs
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Book Synopsis Jump Diffusion Processes: Discrete-time Option Replication and Pricing European Call Options in the Presence of Transaction Costs by : Aurele Mawudo Houngbedji
Download or read book Jump Diffusion Processes: Discrete-time Option Replication and Pricing European Call Options in the Presence of Transaction Costs written by Aurele Mawudo Houngbedji and published by . This book was released on 2000 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whereas the discrete-time hedging strategies and hedging error problems have been examined by several researchers under the Black-Scholes assumption of geometric Brownian motion, nothing has been done to the problems when the stocks have discontinuous returns. This dissertation, examines two major issues in options pricing and hedging: the problem of discrete-time hedging and hedging error on the one hand, and pricing European call options in the presence of transaction costs on the other, when the underlying securities follow a jump-diffusion process. Under the assumptions of the continuous time models presented by Bardhan and Chao (1993), we develop discrete-time hedging strategies using a fixed revision interval and constant parameters for European call option, and analyzed the associated hedging errors associated. We proved that the total hedging error converges to zero in probability as the time between rebalancing points goes to zero. For small revision time intervals, we derive an approximate conditional distribution for the individual one period hedging errors. We derive an exact closed form expression for the total expected hedging error, conditional on the information at time when the call option is written. The results obtained can be used in risk management to monitor the performance of the strategies. We also developed an equation for European call options when the underlying asset follows the jump-diffusion process in the presence of non-zero transaction costs: extending an equation of Leland's (1985).
Book Synopsis Discrete-time Bond and Option Pricing for Jump-diffusion Processes by : Sanjiv R. Das
Download or read book Discrete-time Bond and Option Pricing for Jump-diffusion Processes written by Sanjiv R. Das and published by . This book was released on 1994 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a methodology for pricing American type interest rate contingent claims for jump-diffusion processes. The method enhances the standard finite-differencing approach to deal with partial differential-difference equations derived in a jump-diffusion world. The numerical stability and convergence of the scheme is also proved. Numerical illustrations compare jump-diffusion and pure-diffusion models. Whereas the existence of jumps affects call options on bonds very much like those on stocks, this is not the case for puts which are affected by the asymmetric convexity of the bond pricing function. Early exercise behavior is also analyzed.
Book Synopsis Discrete-time Bond and Option Pricing for Jump-diffusion Processes by : Sanjiv R. Das
Download or read book Discrete-time Bond and Option Pricing for Jump-diffusion Processes written by Sanjiv R. Das and published by . This book was released on 1994 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a methodology for pricing American type interest rate contingent claims for jump-diffusion processes. The method enhances the standard finite-differencing approach to deal with partial differential-difference equations derived in a jump-diffusion world. The numerical stability and convergence of the scheme is also proved. Numerical illustrations compare jump-diffusion and pure-diffusion models. Whereas the existence of jumps affects call options on bonds very much like those on stocks, this is not the case for puts which are affected by the asymmetric convexity of the bond pricing function. Early exercise behavior is also analyzed.
Book Synopsis Discrete-Time Bond and Options Pricing for Jump-Diffusion Processes by : Sanjiv Ranjan Das
Download or read book Discrete-Time Bond and Options Pricing for Jump-Diffusion Processes written by Sanjiv Ranjan Das and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a methodology for pricing American type interest rate contingent claims for jump-diffusion processes. The method enhances the standard finite- differencing approach to deal with partial differential- difference equations derived in a jump-diffusion world. The numerical stability and convergence of the scheme is also proved. Numerical illustrations compare jump-diffusion and pure-diffusion models. Whereas the existence of jumps affects call options on bonds very much like those on stocks, this is not the case for puts which are affected by the asymmetric convexity of the bond pricing functions. Early exercise behavior is also analyzed.
Book Synopsis Option Replication with Transaction Costs - an Exact Solution for the Pure Jump Process by : Anthony Neuberger
Download or read book Option Replication with Transaction Costs - an Exact Solution for the Pure Jump Process written by Anthony Neuberger and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the presence of proportional transactions costs, the tightest bounds which can be imposed on the price of a call option when the asset price follows a geometric diffusion process are those imposed by static portfolio strategies. The price of a call is bounded above by the value of the asset and below by its intrinsic value. However with a pure jump process it is possible to obtain much tighter arbitrage bounds on the value of a contingent claim, which converge to the no transaction cost valuation as transaction costs become small.
Book Synopsis Jump Diffusion Option with Transaction Costs by : Oana Mocioalca
Download or read book Jump Diffusion Option with Transaction Costs written by Oana Mocioalca and published by . This book was released on 2002 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing Under Exponential Jump Diffusion Processes by : Tianren Bu
Download or read book Option Pricing Under Exponential Jump Diffusion Processes written by Tianren Bu and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pricing European Options in Markets With Transaction Costs by : Stepan Sahakyan
Download or read book Pricing European Options in Markets With Transaction Costs written by Stepan Sahakyan and published by . This book was released on 2015 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we propose conceptually new approach to pricing European call options in markets with transaction costs. In contrast to the previous research, we introduce and model two - quote and gross (which includes transaction costs and fees) - price processes. Also using both price processes we introduce new portfolio replication concept, namely "quasi replication" strategy. The advantage of the proposed model is its simplicity, whereby the price of the European option is expressed in terms of the Black-Scholes type formulas.
Book Synopsis Jump Diffusion European Option Pricing and Mellin Transforms by : Rob Shorten
Download or read book Jump Diffusion European Option Pricing and Mellin Transforms written by Rob Shorten and published by . This book was released on 2013 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis African Doctorates in Mathematics by :
Download or read book African Doctorates in Mathematics written by and published by Lulu.com. This book was released on 2007 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a catalogue of over 2000 doctoral theses by Africans in all fields of mathematics, including applied mathematics, mathematics education and history of mathematics. The introduction contains information about distribution by country, institutions, period, and by gender, about mathematical density, and mobility of mathematicians. Several appendices are included (female doctorate holders, doctorates in mathematics education, doctorates awarded by African universities to non-Africans, doctoral theses by non-Africans about mathematics in Africa, activities of African mathematicians at the service of their communities). Paulus Gerdes compiled the information in his capacity of Chairman of the African Mathematical Union Commission for the History of Mathematics in Africa (AMUCHMA). The book contains a preface by Mohamed Hassan, President of the African Academy of Sciences (AAS) and Executive Director of the Academy of Sciences for the Developing World (TWAS). (383 pp.)
Book Synopsis Pricing Options in Jump-Diffusion Models by : Liming Feng
Download or read book Pricing Options in Jump-Diffusion Models written by Liming Feng and published by . This book was released on 2007 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a new computational method for the valuation of options in jump-diffusion models. The option value function for European and barrier options satisfies a partial integro-differential equation (PIDE). This PIDE is commonly integrated in time by implicit-explicit (IMEX) time discretization schemes, where the differential (diffusion) term is treated implicitly, while the integral (jump) term is treated explicitly. In particular, the popular IMEX Euler scheme is first order accurate in time. Second order accuracy in time can be achieved by using the IMEX midpoint scheme. In contrast to the above approaches, we propose a new high-order time discretization scheme for the PIDE based on the extrapolation approach to the solution of ODEs, that also treats the diffusion term implicitly and the jump term explicitly. The scheme is simple to implement, can be added to any PIDE solver based on the IMEX Euler scheme, and is remarkably fast and accurate. We demonstrate our approach on the examples of Merton's and Kou's jump-diffusion models, diffusion-extended Variance Gamma model, as well as the two-dimensional Duffie-Pan-Singleton model with correlated and contemporaneous jumps in the stock price and its volatility. By way of example, pricing a one-year double-barrier option in Kou's jump-diffusion model, our scheme attains accuracy of $10^{-5}$ in 72 time steps (in 0.05 seconds). In contrast, it takes the first-order IMEX Euler scheme more than 1.3 million time steps (in 873 seconds) and the second-order IMEX midpoint scheme 768 time steps (in 0.49 seconds) to attain the same accuracy. Our scheme is also well suited for Bermudan options. Combining simplicity of implementation and remarkable gains in computational efficiency, we expect this method to be very attractive to financial engineering modelers.
Book Synopsis Option Replication with Large Transactions Costs by : Ariane Reiss
Download or read book Option Replication with Large Transactions Costs written by Ariane Reiss and published by . This book was released on 1999 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contrary to a continuous-time model, in a discrete-time binomial model it is possible to construct a self-financing strategy which exactly replicates the payoff of a European option contract at maturity in the presence of proportional transactions costs. We derive an upper boundary for the cost factor in a market where all investors face the same factor. This upper boundary ensures the efficiency of the riskfree bond price as well as the stock price process. It turns out that perfect replication is optimal in the presence of only one transactions costs factor. Furthermore, conditions are given under which superreplicating strategies are dominant under differential transactions costs. A closed-form solution for the value of a Short call option is derived. While this least initial endowment is preference-free, the individual replicating strategy is preference-dependent. In addition, we show how the value of a Long European call option is derived computationally easily.
Book Synopsis Option Replication in Discrete Time with Transaction Costs by : Malene Sun Kim Friis
Download or read book Option Replication in Discrete Time with Transaction Costs written by Malene Sun Kim Friis and published by . This book was released on 2011 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Appendix To: Efficient European and American Option Pricing Under a Jump-diffusion Process by : Marcellino Gaudenzi
Download or read book Appendix To: Efficient European and American Option Pricing Under a Jump-diffusion Process written by Marcellino Gaudenzi and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing on Jump-diffusion Models by :
Download or read book Option Pricing on Jump-diffusion Models written by and published by . This book was released on 2009 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Replication in Discrete Time with Transaction Costs by : Phelim P. Boyle
Download or read book Option Replication in Discrete Time with Transaction Costs written by Phelim P. Boyle and published by . This book was released on 1992 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis McKean's Method Applied to American Call Options on Jump-diffusion Processes by : Carl Chiarella
Download or read book McKean's Method Applied to American Call Options on Jump-diffusion Processes written by Carl Chiarella and published by . This book was released on 2004 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
