Computation of Reservation Prices of Options with Proportional Transaction Costs PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Computation of Reservation Prices of Options with Proportional Transaction Costs PDF full book. Access full book title Computation of Reservation Prices of Options with Proportional Transaction Costs by Anders Damgaard. Download full books in PDF and EPUB format.
Author: Anders Damgaard Publisher: ISBN: Category : Languages : en Pages : 36
Book Description
In this paper we analyze the numerical scheme applied in Damgaard (2000a) to compute reservation prices of European options. In addition, we suggest and implement a procedure for computing reservation purchase prices of American options. In the paper we consider a continuous time economy with proportional transaction costs where the investors are assumed to have finite time horizons and HARA utility functions defined over terminal wealth. In the European case we show that the value functions are unique viscosity solutions of their respective HJB equations. We suggest and implement a discretization scheme for computing reservation prices of European options. This corresponds to solving a highly non-linear pde in time with three state variables. Convergence proofs for the employed discretization schemes are provided, and numerical examples are given. For the case of American call options we give an example showing that the presence of transaction costs implies under some circumstances that it is optimal to exercise an American call option written on a non-dividend paying security before maturity.
Author: Anders Damgaard Publisher: ISBN: Category : Languages : en Pages : 36
Book Description
In this paper we analyze the numerical scheme applied in Damgaard (2000a) to compute reservation prices of European options. In addition, we suggest and implement a procedure for computing reservation purchase prices of American options. In the paper we consider a continuous time economy with proportional transaction costs where the investors are assumed to have finite time horizons and HARA utility functions defined over terminal wealth. In the European case we show that the value functions are unique viscosity solutions of their respective HJB equations. We suggest and implement a discretization scheme for computing reservation prices of European options. This corresponds to solving a highly non-linear pde in time with three state variables. Convergence proofs for the employed discretization schemes are provided, and numerical examples are given. For the case of American call options we give an example showing that the presence of transaction costs implies under some circumstances that it is optimal to exercise an American call option written on a non-dividend paying security before maturity.
Author: Erling Dalgaard Andersen Publisher: ISBN: Category : Languages : en Pages :
Book Description
The purpose of the present work is to examine the financial problem of finding the reservation purchase price of a European call option written on a risky security when there is proportional transaction costs in the market. Existing papers within this area have all simplified the analysis by considering only one risky security and assumed exponential utility functions. The goal of the present paper is to suggest an approach to compute the reservation price of an option in an economy with more than one risky security and where trade involves transaction costs. Furthermore, the new approach enables us to investigate to what extent the above mentioned simplifications affect the reservation prices. We consider an economy with a riskless security, two risky securities, and agents with HARA utility functions. We suggest an approach to compute reservation prices using convex optimization. Unfortunately, the proposed optimization models become large in terms of the number of constraints and variables. However, using a newly developed interior-point algorithm, we manage to solve problems of an interesting size. The major findings are: (i) the investor's reservation purchase price of a European call option is almost insensitive to the functional form of the utility function, but sensitive (only slightly) to the initial level of absolute risk aversion, and (ii) the presence of diversification opportunities does not affect the reservation price in any unique way.interior-point optimization, reservation prices of options, optimal portfolio choice, diversification.
Author: Valeriy Zakamulin Publisher: ISBN: Category : Languages : en Pages : 40
Book Description
In this paper we examine the problem of finding the reservation option prices and corresponding exercise policies of American options in a market with proportional transaction costs using the utility based approach proposed by Davis and Zariphopoulou (1995). We present a model where the option holder has a constant absolute risk aversion. We discuss the numerical algorithm and propose a new characterization of the option holder's value function. We suggest original discretization schemes for computing reservation prices and exercise policies of American options. The discretization schemes are implemented for the cases of American put and call options. We present the study of the optimal transaction policy of the option holder. We examine the effects on the reservation option prices and the corresponding exercise policies of varying the levels of absolute risk aversion and transaction costs.
Author: Ivan Dimov Publisher: Springer ISBN: 3319202391 Category : Computers Languages : en Pages : 443
Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Finite Difference Methods, FDM 2014, held in Lozenetz, Bulgaria, in June 2014. The 36 revised full papers were carefully reviewed and selected from 62 submissions. These papers together with 12 invited papers cover topics such as finite difference and combined finite difference methods as well as finite element methods and their various applications in physics, chemistry, biology and finance.
Author: Stylianos Perrakis Publisher: ISBN: Category : Languages : en Pages : 48
Book Description
We derive a reservation purchase price for a call option price under proportional transaction costs. The price is derived in discrete time for a general distribution of the returns of the underlying asset, as in Constantinides and Perrakis (CP, 2002, 2007). We then consider a lognormal diffusion model of these returns, and we formulate a discrete time trading version that converges to diffusion as the time partition becomes progressively more dense. Given the existence of a partition-independent and tight upper bound already derived in CP (2002), we focus on the lower bound. We show that the CP approach results in a lower bound for European call options that converges to a non-trivial and tight limit that is a function of the transaction cost parameter. This limit defines a reservation purchase price under realistic trading conditions for the call options and becomes equal to the exact Black-Scholes-Merton value if the transaction cost parameter is set equal to zero. We also develop a novel numerical algorithm that computes the CP lower bound for any discrete time partition and converges to the theoretical continuous time limit in a relatively small number of iterations. Last, we extend the lower bound results to American index and index futures options.
Author: Matthias Ehrhardt Publisher: Springer ISBN: 3319612824 Category : Mathematics Languages : en Pages : 599
Book Description
This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector. The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models. In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techniques are now essential to the majority of present-day applications in the financial industry. Special attention is devoted to a uniform methodology for both testing the latest achievements and simultaneously educating young PhD students. Most of the mathematical codes are linked into a novel computational finance toolbox, which is provided in MATLAB and PYTHON with an open access license. The book offers a valuable guide for researchers in computational finance and related areas, e.g. energy markets, with an interest in industrial mathematics.
Author: Alet Roux Publisher: VDM Publishing ISBN: 9783836492393 Category : Algorithms Languages : en Pages : 0
Book Description
This book is aimed at researchers and PhD students in mathematical finance. It studies the pricing and hedging of options in financial markets with proportional transaction costs on trading in shares, modeled as bid-ask spreads, and different interest rates for borrowing and lending of cash. This is done by means of fair pricing and super-hedging. The fair price of an option is any market price for it that does not allow traders to make profit with no risk, and a super-hedging strategy allows the seller and buyer to remain in a solvent position after respectively delivering and receiving the option payoff. Efficient algo-rithms are presented for computing the bid and ask prices of European and American options; these prices serve as bounds on the fair prices. This unifies all existing algorithms for the calculation of such prices. As a by-product, a straightforward iterative method is found for determining the optimal super-hedging strategies (and stopping times) for both the buyer and seller of an option, and also optimal stopping strategies in the case of American options.
Author: Cheng Few Lee Publisher: World Scientific ISBN: 9811202400 Category : Business & Economics Languages : en Pages : 5053
Book Description
This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.
Author: Anders Damgaard
Author: Anders Damgaard
Author: Erling Dalgaard Andersen
Author: Valeriy Zakamulin
Author: Ivan Dimov
Author: 
Author: George M. Constantinides
Author: Stylianos Perrakis
Author: Matthias Ehrhardt
Author: Alet Roux
Author: Cheng Few Lee