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.
European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs
Author: Valeriy ZakamulinPublisher:
ISBN:
Category :
Languages : en
Pages : 27
Book Description
In this paper we provide a systematic treatment of the utility based option pricing and hedging approach in markets with both fixed and proportional transaction costs: We extend the framework developed by Davis, Panas and Zariphopoulou (1993) and formulate the option pricing and hedging problem. We propose and implement a numerical procedure for computing option prices and corresponding optimal hedging strategies. We present a careful analysis of the optimal hedging strategy and elaborate on important differences between the exact hedging strategy and the asymptotic hedging strategy of Whaley and Wilmott (1994). We provide a simulation analysis in order to compare the performance of the utility based hedging strategy against the asymptotic strategy and some other common strategies.
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.
European Option Pricing with General Transaction Costs and Short-Selling Constraints
Author: Ajay SubramanianPublisher:
ISBN:
Category :
Languages : en
Pages : 63
Book Description
In this paper, we study the problem of European Option Pricing in a market with short-selling constraints and transaction costs having a very general form. We consider two types of proportional costs and a strictly positive fixed cost. We study the problem within the framework of the theory of stochastic impulse control. We show that determining the price of a European option involves calculating the value functions of two stochastic impulse control problems. We obtain explicit expressions for the quasi-variational inequalities satisfied by the value functions and derive the solution in the case where the parameters of the price processes are constants and the investor's utility function is linear. We use this result to obtain a price for a call option on the stock and prove that this price is a nontrivial lower bound on the hedging price of the call option in the presence of general transaction costs and short-selling constraints. We then consider the situation where the investor's utility function has a general form and characterize the value function as the pointwise limit of an increasing sequence of solutions to associated optimal stopping problems. We thereby devise a numerical procedure to calculate the option price in this general setting and implement the procedure to calculate the option price for the class of exponential utility functions. Finally, we carry out a qualitative investigation of the option prices for exponential and linear-power utility functions.
European Option Pricing with Transaction Costs
Author: Asadullah JawidUtility Based Option Pricing with Proportional Transaction Costs and Diversification Problems
Author: Erling Dalgaard AndersenPublisher:
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.
European 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.
Author: Erling D. Andersen