Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 179
Book Description
European and American Options Under Proportional Transaction Costs
Author: European Options Under Proportional Transaction Costs
Author: Alet RouxPublisher:
ISBN:
Category :
Languages : en
Pages : 20
Book Description
The paper is devoted to optimal superreplication of European options in the discrete setting under proportional transaction costs on the underlying asset. In particular, general pricing and hedging algorithms are developed. This extends previous work by many authors, which has been focused on the binomial tree model and options with specific payoffs such as calls or puts, often under certain bounds on the magnitude of transaction costs. All such restrictions are hereby removed. The results apply to options with arbitrary payoffs in the general discrete market model with arbitrary proportional transaction costs. Numerical examples are presented to illustrate the results and their relationships to the earlier work on pricing options under transaction costs.
Options Under Transaction Costs
Author: Alet RouxPublisher: 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.
American Options Under Proportional Transaction Costs
Author: Tomasz ZastawniakPublisher:
ISBN:
Category :
Languages : en
Pages : 24
Book Description
American options are priced and hedged in a general discrete market in the presence of arbitrary proportional transaction costs inherent in trading the underlying asset, modelled as bid-ask spreads. Pricing, hedging and optimal stopping algorithms are established for a short position (seller's position) in an American option with an arbitrary payoff settled by physical delivery. The seller's price representation as the expectation of the stopped payoff under an approximate martingale measure is also considered. The algorithms cover and extend the various special cases considered in the literature to-date. Any specific restrictions that were imposed on the form of the payoff, the magnitude of transaction costs or the discrete market model itself are relaxed. The pricing algorithm under transaction costs can be viewed as a natural generalisation of the iterative Snell envelope construction.
Markets with Transaction Costs
Author: Yuri KabanovPublisher: Springer Science & Business Media
ISBN: 3540681213
Category : Business & Economics
Languages : en
Pages : 306
Book Description
The book is the first monograph on this highly important subject.
Computation of Reservation Prices of Options with Proportional Transaction Costs
Author: Anders DamgaardPublisher:
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.
Numerical Methods for the Solution of the HJB Equations Arising in European and American Option Pricing with Proportional Transaction Costs
Author: Wen LiPublisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 102
Book Description
This thesis is concerned with the investigation of numerical methods for the solution of the Hamilton-Jacobi-Bellman (HJB) equations arising in European and American option pricing with proportional transaction costs. We first consider the problem of computing reservation purchase and write prices of a European option in the model proposed by Davis, Panas and Zariphopoulou [19]. It has been shown [19] that computing the reservation purchase and write prices of a European option involves solving three different fully nonlinear HJB equations. In this thesis, we propose a penalty approach combined with a finite difference scheme to solve the HJB equations. We first approximate each of the HJB equations by a quasi-linear second order partial differential equation containing two linear penalty terms with penalty parameters. We then develop a numerical scheme based on the finite differencing in both space and time for solving the penalized equation. We prove that there exists a unique viscosity solution to the penalized equation and the viscosity solution to the penalized equation converges to that of the original HJB equation as the penalty parameters tend to infinity. We also prove that the solution of the finite difference scheme converges to the viscosity solution of the penalized equation. Numerical results are given to demonstrate the effectiveness of the proposed method. We extend the penalty approach combined with a finite difference scheme to the HJB equations in the American option pricing model proposed by Davis and Zarphopoulou [20]. Numerical experiments are presented to illustrate the theoretical findings.
European Option Pricing with Transaction Costs
Author: Asadullah JawidEuropean Option Pricing with Fixed Transaction Costs
Author: Ajay Subramanian AiyerPublisher:
ISBN:
Category : Options (Finance)
Languages : en
Pages : 30
Book Description
Pricing European Options in Markets With Transaction Costs
Author: Stepan SahakyanPublisher:
ISBN:
Category :
Languages : en
Pages : 9
Book Description
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.